Answer: 9x^2+30x+25 ---------- Perimeter of a square is the sum of the 4 equal sides, which is given as 12x + 20. Therefore, each side = 12x + 20 ------ = 3x + 5 4 The area of the square is (3x + 5)^2 (3x+5)(3x+5) 9x^2 + 30x + 25
Perimeter = 12x + 20 Thetefore side length = (12x + 20)/4 = 3x + 5 Therefore area = (3x + 5)² Doesn't seem any point in multiplying that out. Seems cleaner and simpler to leave it as that.
Easy. Let’s go. If a polygon is a square, it must have four right angle measures (assuming flat space) and four equal sides. The area of such a square is given as A = s^2, where A is the area and s is the measure of one side of the square. In this case, we aren’t given a side measure, but we are given the perimeter of the square. The perimeter of a square is P = 4s, where P is the perimeter of the square. We can now solve for s, which is in terms of x in this example: 12x + 20 = 4s s = (12x + 20) / 4 s = 4(3x + 5) / 4 s = 3x + 5 Now that we have s, we can get A: A = s^2 = (3x + 5)^2 = 9x^2 + 30x + 25 square units And this is the area.
Perimeter of a Square = side + side + side + side = 4 · side ,btw side = side Area of a Square = side · side = side² Given: Perimeter = 12x + 20 --> 4 · side [12x + 20] / 4 = 4[3x + 5] / 4 = 3x +5 --> 1 side side = side --> 3x + 5 = 3x + 5 Asked : Area(square) = side · side Area(square) = [3x + 5]² = 9x² + 30x + 25 --> in terms of x✅ merkwaardige product : (a + b)² = a² + 2(ab) + b²
I got the correct answer: 9x^2 + 30x +25. However, he asked for area "in terms of x" so I continued on to solve for x using the quadratic formula and got a nonsense answer: " -30 +/- sq rt of 0/18 ". Why can't I find X ?? Why does the Quad formula not work? Anybody know?
The quadratic formula is for solving a quadratic equation, and this is not an equation. The purpose of the formula you are trying to use is to find the value(s) of x when you have an equation of the form ax² + bx + c = 0 Why would the 9x² + 30x + 25 here be equal to 0?
@@gavindeane3670 Well. it is an equation. 9x² + 30x − a + 25 = 0 Where a = area. I'm pretty sure a two variable quadratic is solvable for at least one of the variables, but I've got no idea how. BTW, Terry, If we solve 9x² + 30x + 25 = 0 we get x= −30/18. Since all the gumph after the ± in the denominator becomes zero, we can just ditch it. It's not the answer to the problem John set, but yeah: if that was a one variable quadratic, x would equal −1.666. An unusual one, too, since there's only one possible answer.
@@dazartingstall6680 The answer to the question in the video is 9x² + 30x + 25 = area It's just an expression of the area in terms of x. Having found that, we *could* ask a supplementary question, which is: given a value for the area, what is the value of x? To answer that, we construct the equation 9x² + 30x + 25 = and solve it like any quadratic. So by choosing to write 9x² + 30x + 25 = 0 and solving for x, we are answering the question: what is the value of x when the area of the square is 0. But there's nothing special about 0. We could do that for any area value. What is the value of x if the area is 10? Solve 9x² + 30x + 25 = 10 What is the value of x if the area is 1000? Solve 9x² + 30x + 25 = 1000 What is the value of x if the area is 258.531? Solve 9x² + 30x + 25 = 258.531 What is the value of x if the area is 2x + 10? Solve 9x² + 30x + 25 = 2x + 10 The question asks for a general expression of area in terms of x. Another supplementary thing we could do is to turn that into a general expression of x in terms of the area by simply writing the quadratic formula with a = 9, b = 30 and c = 25 - area. That assumes that "area" is a numerical value though. It would be a bit more complicated for a case like my area = 2x + 10 example.
@@gavindeane3670 Thanks for your responses. I get your point. I created an equation by inserting "= 0" arbitrarily. What threw me off was John's phrasing the goal "in terms of X". Since we're always solving these problems to find that one unknown, usually called X, I tried to do just that. This seems to be a fine semantic point in word problems of which I was unaware. Combined with John's insistence of always simplifying your answer as much as possible, that final quadratic equation looked too complex to be the correct or final answer. I don't recall any vids in which the difference between expression and equation were explained this way. Silly me. :)
The question in the video title is clear that he's asking for the area in terms of x, so (3x + 5)² is the answer. Or 9x² + 30x + 25 if you prefer. A mismatch between the question in the video thumbnail image and the question in the video title text isn't uncommon on this channel.
Answer: 9x^2+30x+25
----------
Perimeter of a square is the sum of the 4 equal sides, which is given as 12x + 20.
Therefore, each side =
12x + 20
------ = 3x + 5
4
The area of the square
is (3x + 5)^2
(3x+5)(3x+5)
9x^2 + 30x + 25
I got the right answer, and carried on down the rabbit hole of trying to find the roots. Without realising that I actually didn't need to.
Not only do you not need to, but more importantly the idea of finding the roots makes no sense when we don't know what the actual area is.
9x^2+30x+25
got your answer. that part was easy. tried to solve it as a QE = 0 sr 0 nulifies everything.
fun trying, thanks.
Perimeter = 4 . Length so P = 4L = 12x + 20 -> L = 3x + 5 and Area = L² = 9x² + 30x + 25 units²
Perimeter = 12x + 20
Thetefore side length = (12x + 20)/4
= 3x + 5
Therefore area = (3x + 5)²
Doesn't seem any point in multiplying that out. Seems cleaner and simpler to leave it as that.
square of sides = S
perimeter = 4S
area = S^2
perimeter = 12X+ 20
S = (12X+20)/4
= 3X+5
Area = S^2
=(3X+5)^2
= 9X^2+30X+25
I'm glad I had a Math teacher able to explain such simple things much faster ;-)
A(x)=(3x+5)^2
Also generally the area is a positive value 3x+5=0
3x=-5
x=-(5/3)
x is valid for all numbers greater than
-(5/3)
Easy. Let’s go.
If a polygon is a square, it must have four right angle measures (assuming flat space) and four equal sides. The area of such a square is given as
A = s^2, where A is the area and s is the measure of one side of the square.
In this case, we aren’t given a side measure, but we are given the perimeter of the square. The perimeter of a square is
P = 4s, where P is the perimeter of the square.
We can now solve for s, which is in terms of x in this example:
12x + 20 = 4s
s = (12x + 20) / 4
s = 4(3x + 5) / 4
s = 3x + 5
Now that we have s, we can get A:
A = s^2
= (3x + 5)^2
= 9x^2 + 30x + 25 square units
And this is the area.
Thank you
Perimeter of a Square = side + side + side + side = 4 · side ,btw side = side
Area of a Square = side · side = side²
Given: Perimeter = 12x + 20 --> 4 · side
[12x + 20] / 4 = 4[3x + 5] / 4 = 3x +5 --> 1 side
side = side --> 3x + 5 = 3x + 5
Asked : Area(square) = side · side
Area(square) = [3x + 5]² = 9x² + 30x + 25 --> in terms of x✅
merkwaardige product : (a + b)² = a² + 2(ab) + b²
So u have a negative perimeter but a positive area? What is this House of Leaves?
Why do you think the perimeter is negative?
Area = ((12x + 20)/4)²
= (3x + 5)²
= (3x + 5)(3x + 5)
= 9x² + 15x + 15x + 25
= (9x² + 30x + 25) units²
ar.=(3x+5)^2=9x^2+30x+25.sq.unit where x is variable.ans
Could'nt you split the square into two triangles and get the answer?
However, The answer you derived is no simpler than the original statement.
I got the correct answer: 9x^2 + 30x +25. However, he asked for area "in terms of x" so I continued on to solve for x using the quadratic formula and got a nonsense answer: " -30 +/- sq rt of 0/18 ". Why can't I find X ?? Why does the Quad formula not work? Anybody know?
Because there's two unknowns in the equation. The area and the value of x.
The quadratic formula is for solving a quadratic equation, and this is not an equation.
The purpose of the formula you are trying to use is to find the value(s) of x when you have an equation of the form
ax² + bx + c = 0
Why would the 9x² + 30x + 25 here be equal to 0?
@@gavindeane3670 Well. it is an equation.
9x² + 30x − a + 25 = 0
Where a = area.
I'm pretty sure a two variable quadratic is solvable for at least one of the variables, but I've got no idea how.
BTW, Terry, If we solve
9x² + 30x + 25 = 0
we get x= −30/18. Since all the gumph after the ± in the denominator becomes zero, we can just ditch it. It's not the answer to the problem John set, but yeah: if that was a one variable quadratic, x would equal −1.666. An unusual one, too, since there's only one possible answer.
@@dazartingstall6680
The answer to the question in the video is
9x² + 30x + 25 = area
It's just an expression of the area in terms of x.
Having found that, we *could* ask a supplementary question, which is: given a value for the area, what is the value of x?
To answer that, we construct the equation
9x² + 30x + 25 =
and solve it like any quadratic.
So by choosing to write
9x² + 30x + 25 = 0
and solving for x, we are answering the question: what is the value of x when the area of the square is 0.
But there's nothing special about 0. We could do that for any area value.
What is the value of x if the area is 10? Solve
9x² + 30x + 25 = 10
What is the value of x if the area is 1000? Solve
9x² + 30x + 25 = 1000
What is the value of x if the area is 258.531? Solve
9x² + 30x + 25 = 258.531
What is the value of x if the area is 2x + 10? Solve
9x² + 30x + 25 = 2x + 10
The question asks for a general expression of area in terms of x. Another supplementary thing we could do is to turn that into a general expression of x in terms of the area by simply writing the quadratic formula with a = 9, b = 30 and c = 25 - area. That assumes that "area" is a numerical value though. It would be a bit more complicated for a case like my area = 2x + 10 example.
@@gavindeane3670 Thanks for your responses. I get your point. I created an equation by inserting "= 0" arbitrarily. What threw me off was John's phrasing the goal "in terms of X". Since we're always solving these problems to find that one unknown, usually called X, I tried to do just that. This seems to be a fine semantic point in word problems of which I was unaware. Combined with John's insistence of always simplifying your answer as much as possible, that final quadratic equation looked too complex to be the correct or final answer. I don't recall any vids in which the difference between expression and equation were explained this way. Silly me. :)
=2400 sqf
The square of (3x + 5).
2
The area you come up with needs a value for X you have no value for the area so its not the answer.
The question in the video title is clear that he's asking for the area in terms of x, so (3x + 5)² is the answer. Or 9x² + 30x + 25 if you prefer.
A mismatch between the question in the video thumbnail image and the question in the video title text isn't uncommon on this channel.
15x squared