Thank you for the vid! :D Helped me with the last two steps. Just wanted to point out, even though I there are a LOT of ways you can go about this problem. You can use formula for the area of an eq. ▲, A=(x^2√3)/4, with L for side x. Set it eq. to formula for the area of any ▲, A=(b·h)/2. You get the formula for height of an eq. ▲, h=(L√3)/(2). Then, set the base and height of two inscribed ▲'s eq. to each other and get the rectangle height with x and constant L: y=(√3/2)(L-2x) You're great! :)
I wish you were my calc teacher. You can tell you really know what you are doing because you make it so simple. Thank you so much for posting these helpful videos!
What you're asking for is exactly what she is solving for from 8:10 all the way to the end of the video. Half the rectangle there at 8:10 means that we are optimizing to find the largest rectangle inscribed in a right triangle with hypotenuse L and base L/2 (which is just a special right triangle). Hope that helps Akhil Gupta! Nice video integralCALC!
this problem gave me a headache but nonetheless, thank you so much for your help! ((still think I'm not ready for my exam I hate optimization problems so much))
Please solve this Tree sides of a triangle are 18 cm, 20 cm and 34 cm.find the area of a rectangle of Max area that can be inscribed in this triangle on side 34 cm as a base.
Best explanation of optimization I have ever seen, great work! I have a feeling I am going to turn to your channel a lot throughout the school year. Thanks so much for the help!
I haven't really done the math but.. I'm wondering if we could just solve for one half of the triangle, perhaps the Right Half, and find the values for X and H .. and due to symmetry you can extend those values to the other half of the equilateral triangle. The only difference would be that you double the X value obtained in the Right Half.. the H value would still be the same. Yes? No? Maybe So?..... lol, perhaps I'd best do the math now and see for myself... Thanks Krista for a great video and for fostering a "Thinking Beyond the Problem" .. :) .. Peace always...
plot a rectangle which lies in first quadrant has one vertex is 6 units long along x- axis and 4unit long along y-axis .give the coordinates of its vertices solve this question
My lecturer give similar question as in the video but she changes from equilateral triangle to right triangle, do I should use the same solving method to get the answer?
you have chose the hardest way, there are planetary of easier way to solve the problem. e.g. take the linear equation for right triangle then multiply area by 2
ur video really helps me a lot..can ask u something on ANAGEO, i cant answer it even i searched it on google haha..Two vertices of an equilateral triangle are (0,0) and (5,5). find the slopes of the 3 sides? plss helps me make a video about this question plssss
Thanks for your help this problem is dreadful! Why can you use half the rectangle for optimization @ 7:55 ? I get that if you use A=2x(h) you get the same value for x when you do the derivative, but then later when you multiply by 2 @ 11:13 it messes up the value doesn't it? Thanks again this problem seemed hopeless before I found this video.
Why would it mess it up @ 11:13? When we multiply by 2, we're just taking what we know about half of the base, and changing it so that it's related to the entire base. :)
Because the length of the entire base is b, and we know the rectangle is symmetric about the y-axis, which means the length of the base to the left of the y-axis has to be half of the base, and same with the length of the base to the right of the y-axis. So b/2 and b/2. :)
I have a question. If x = b/2, then b = 2x, so we when you change the area equation so that it is in terms of x, don't you write A = 2x( (sqrt3)L/2 - (sqrt3)x). You only put one x and that isn't really making sense to me since x is b/2, or am I missing something?
Hi, Can you pls tell me what are u using to write on that board? Are u using a kinda software to make this video tutorial... I need to make a tutorial like this...I would be writing while explaining... I want to do that for students living in Africa. Your help and respond would be greatly appreciated
Even 9 years later, your video continues to be of great service. Thank you!
You're welcome, Daniel, I'm happy to help!
Thank you for the vid! :D
Helped me with the last two steps.
Just wanted to point out, even though I there are a LOT of ways you can go about this problem.
You can use formula for the area of an eq. ▲, A=(x^2√3)/4, with L for side x. Set it eq. to formula for the area of any ▲, A=(b·h)/2. You get the formula for height of an eq. ▲, h=(L√3)/(2).
Then, set the base and height of two inscribed ▲'s eq. to each other and get the rectangle height with x and constant L: y=(√3/2)(L-2x)
You're great! :)
I wish you were my calc teacher. You can tell you really know what you are doing because you make it so simple. Thank you so much for posting these helpful videos!
+Pamela Martin I'm glad they're helping, and hopefully they can fill in the gaps if your calc teacher doesn't explain everything!
If this questions appears on my final im gonna spontaneously combust
This problem is genuinely horrible
Agreed. Optimization problems are the bane of my existence
You are the smartest and prettiest mathematician on youtube. Thanks for this video!!
What you're asking for is exactly what she is solving for from 8:10 all the way to the end of the video. Half the rectangle there at 8:10 means that we are optimizing to find the largest rectangle inscribed in a right triangle with hypotenuse L and base L/2 (which is just a special right triangle). Hope that helps Akhil Gupta! Nice video integralCALC!
Krista King is STILL the QUEEN of Calculus!! :)
In all my years of high school/college you've been the best and most helpful calculus teacher I've ever had. Thank you.
Aww, thanks!
Thank you so much! I'm studying for my calc final this week and I've never understood how to symbolically solve optimization problems like these.
hardest question ive ever seen in my life!
Thanks a lot Krista. I was stuck with this problem and couldn't find someone explain it to me. You did an awesome job.
Thank you so much, I'm so glad I was able to help!
Great study tool for my calc test tomorrow. Thanks for saving my grade!
I hope your test goes well!
Got stumped by this question on a Calc quiz. Thanks for explaining it so well!
Ah, I wish you could've has seen this beforehand, but I'm glad it could still help!
this problem gave me a headache but nonetheless, thank you so much for your help! ((still think I'm not ready for my exam I hate optimization problems so much))
Optimization problems are super tough, but they just take a lot of practice. So keep working on them, and they'll get easier! Good luck on your exam!
These are SUPER confusing!! Hopefully watching it a couple of times makes it seem a little easier!! :D
Once again you've helped me with Calculus ! Thank you!!!
:D
Thank you so much! This helped immensely. I had no idea how to approach this problem!
thank you soooo much! that was really helpful. i find the optimization hard but your explanations and work are very thorough!
I'm glad I can help!
You're so welcome! :D Hope it goes well!
Thanks for this video. Quite a lot of variables going on!
one small incorrect. b = 2x, not x, when sub into Area function. but the final answer is same. and thank you for the video, that is so helpful.
Please solve this
Tree sides of a triangle are 18 cm, 20 cm and 34 cm.find the area of a rectangle of Max area that can be inscribed in this triangle on side 34 cm as a base.
Best explanation of optimization I have ever seen, great work! I have a feeling I am going to turn to your channel a lot throughout the school year. Thanks so much for the help!
I'm so glad it helped! The videos will be here whenever you need them. :D
So glad i found your channel. Thank you.
+nicholas williams I'm so glad you did too!
I haven't really done the math but.. I'm wondering if we could just solve for one half of the triangle, perhaps the Right Half, and find the values for X and H .. and due to symmetry you can extend those values to the other half of the equilateral triangle. The only difference would be that you double the X value obtained in the Right Half.. the H value would still be the same. Yes? No? Maybe So?..... lol, perhaps I'd best do the math now and see for myself... Thanks Krista for a great video and for fostering a "Thinking Beyond the Problem" .. :) .. Peace always...
i have a question - what is the use of higher order derivative test?
Thank you so much
You're welcome, rekha! :)
Awesome! Thanks! :D
Any chance we can get some Linear Algebra?
How can we find the largest area of squre inside scalen triangle
can you make a similar video for the maximum area of a rectangle which can be inscribed in a triangle of area M ? or generalized
Very much needed THANKS, triangle inequalities getting me again!
+Nick Cooley Glad I could help!
You're a great teacher!
Aw thanks!
I'm just glad I can help. :)
THANK YOU! I was tutoring a boy from high school and couldn't get the right variables ! Thanks!
+qareyida You're welcome, I'm so glad I could help! :D
thanks a lot for this..could you please do for biggest square in a right triangle though..
This video was SOOOOOOOO helpful. Thanks a bunch!
+Diego Pantoja You're welcome, I'm so glad it helped!
plot a rectangle which lies in first quadrant has one vertex is 6 units long along x- axis and 4unit long along y-axis .give the coordinates of its vertices solve this question
thanks krista love you
You're ike the best looking math teacher ever! Thank for the videos .
Oh boy....this gave me a headache. But very helpful indeed. Thank you.
Love you channel :). Can you please do a video to determine the area of the largest rectangle that can be inscribed in a right triangle?
Wow. You blow my mind! Unfortunately, mathematically...
Just great job!
Thanks!
Thank you so much! Optimization problems are so much fun! :)
Beautifully done! :)
You are an actual angel!!!! Thank you so so much🙌🏻
I do not quite understand why you did not consider the length of the rectangle as 2x rather than x at 8:19, that got me confused.
thank you so much you are literally saved my life
So glad I could help! :)
My lecturer give similar question as in the video but she changes from equilateral triangle to right triangle, do I should use the same solving method to get the answer?
+shakur cresendo You could use either one, whichever one makes more sense to you! :)
Thank you so much!! It was really helpful.
you have chose the hardest way, there are planetary of easier way to solve the problem. e.g. take the linear equation for right triangle then multiply area by 2
I was thinking the same thing. The problem could have been done a lot faster and in a more easily understood way
ur video really helps me a lot..can ask u something on ANAGEO, i cant answer it even i searched it on google haha..Two vertices of an equilateral triangle are (0,0) and (5,5). find the slopes of the 3 sides? plss helps me make a video about this question plssss
Cheers lass.
:)
Thanks. I appreciate the assist.
I think that's always the case with optimization problems!! :)
you're welcome!! :)
thanks very good
Thanks, Deleon! :)
Thank you!! I will try! :)
Thanks! :)
I´m your fan, you really did a great job!!!. thanks in advance
Still helping out 7 years later 💪
Yess
Thanks for your help this problem is dreadful! Why can you use half the rectangle for optimization @ 7:55 ? I get that if you use A=2x(h) you get the same value for x when you do the derivative, but then later when you multiply by 2 @ 11:13 it messes up the value doesn't it? Thanks again this problem seemed hopeless before I found this video.
Why would it mess it up @ 11:13? When we multiply by 2, we're just taking what we know about half of the base, and changing it so that it's related to the entire base. :)
I think I get thanks for your help again with this problem!
Amazing explanation. Very clear. Thank you!!!
+Jeffrey Mann You're welcome, I'm so glad you liked it!
Thank you so much.... your awesome
Doing isosceles triangle now
Good video, but those letters is confusing me a lot. I have to watch it few times.
you're welcome!! :D
I thought the largest rectangle that would fit in a triangle is a square? So that's not the case?
I want to find the area of triangle with 3d like i+2j+3k and -3i-2j+k plz.
thanks!
You're welcome! Glad it could help.
Absolutely as always!
Hare Krishna Hare Krishna Krishna Krishna Hare Hare
Hare Ram Hare Ram Ram Ram Hare Hare
How did you record this ? Ipad? Digitizer?
I use a program called Screenflow to record my screen when I'm making these videos. :)
@@kristakingmath thanks for the reply. And the corkboard effect is included too ? :)
For the foreseeable future I'll be focused on just calc I & II. Sorry about that!
Thank you for putting this video up, you have more than earned a sub my dear friend :D
calculus can tend to do that :)
Good deal! :)
thx
You're welcome, jj! :)
thanks for this vid :D
Harder question would be for an isosceles triangle that is not equilateral. That’s what I’m stuck with.
Almost died of stroke trying to figure this out.........Thanks
How did you know you had to split b into 2?
Because the length of the entire base is b, and we know the rectangle is symmetric about the y-axis, which means the length of the base to the left of the y-axis has to be half of the base, and same with the length of the base to the right of the y-axis. So b/2 and b/2. :)
THANK THE LORD THIS CHANNEL EXISTS
This was awesome. thank you!
You're welcome, I'm so glad you liked it!
God help me if this type of question is on my upcoming exam
b=x or 2x please can help me
thank you!!!!
+crazybigyo You're welcome!
I have a question. If x = b/2, then b = 2x, so we when you change the area equation so that it is in terms of x, don't you write A = 2x( (sqrt3)L/2 - (sqrt3)x). You only put one x and that isn't really making sense to me since x is b/2, or am I missing something?
if this problem is on the final, i will be very upset.
Was it?
Ah, nevermind. You get the same value for x whether you put x or 2x. Can you explain why that works?
SALUTE! YOU'RE GENIUS! I HOPE TO BE AS GOOD AS YOU!
who the hell could dislike optimization? :DDDD
Right?! :)
I LIKE IT PICASSO, YEA DAT WAY. Thank you for this video lol
Hi, Can you pls tell me what are u using to write on that board? Are u using a kinda software to make this video tutorial...
I need to make a tutorial like this...I would be writing while explaining... I want to do that for students living in Africa.
Your help and respond would be greatly appreciated
+Michael Bernard This is everything I use to make my videos: learn.calculusexpert.com/my-videos
CalculusExpert.com Wow...This is very helpful...I dont know how to thank you.... You are so awesome...Thanks a million
Wow there are so much steps involved, at least the product rule for the derivative cut me some steps.
her eyes went o.0
this helped quite a bit....and btw ur such a babe...
Thanks
Wtf did I just watch