A square has a perimeter = 12x + 20. What is the AREA in terms of x? Basic Algebra and Geometry

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  • Опубліковано 11 січ 2025

КОМЕНТАРІ • 31

  • @chrisdissanayake6979
    @chrisdissanayake6979 21 день тому +3

    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

  • @DCOneFourSeven
    @DCOneFourSeven 21 день тому +1

    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.

    • @gavindeane3670
      @gavindeane3670 21 день тому +1

      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.

  • @josephlaura7387
    @josephlaura7387 21 день тому +3

    9x^2+30x+25

  • @russelllomando8460
    @russelllomando8460 21 день тому

    got your answer. that part was easy. tried to solve it as a QE = 0 sr 0 nulifies everything.
    fun trying, thanks.

  • @panlomito
    @panlomito 10 днів тому

    Perimeter = 4 . Length so P = 4L = 12x + 20 -> L = 3x + 5 and Area = L² = 9x² + 30x + 25 units²

  • @gavindeane3670
    @gavindeane3670 21 день тому

    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.

  • @tomtke7351
    @tomtke7351 21 день тому +1

    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

  • @markdevries670
    @markdevries670 21 день тому

    I'm glad I had a Math teacher able to explain such simple things much faster ;-)

  • @TSSolutionsPro
    @TSSolutionsPro 20 днів тому

    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)

  • @stevendebettencourt7651
    @stevendebettencourt7651 21 день тому

    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.

  • @raya.pawley3563
    @raya.pawley3563 21 день тому

    Thank you

  • @Stylux-z1p
    @Stylux-z1p 21 день тому

    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

  • @chris-hj2qd
    @chris-hj2qd 21 день тому

    So u have a negative perimeter but a positive area? What is this House of Leaves?

    • @gavindeane3670
      @gavindeane3670 21 день тому

      Why do you think the perimeter is negative?

  • @dazartingstall6680
    @dazartingstall6680 21 день тому

    Area = ((12x + 20)/4)²
    = (3x + 5)²
    = (3x + 5)(3x + 5)
    = 9x² + 15x + 15x + 25
    = (9x² + 30x + 25) units²

  • @adgf1x
    @adgf1x 21 день тому

    ar.=(3x+5)^2=9x^2+30x+25.sq.unit where x is variable.ans

  • @richardpetersen2747
    @richardpetersen2747 20 днів тому

    Could'nt you split the square into two triangles and get the answer?

  • @clems6989
    @clems6989 20 днів тому

    However, The answer you derived is no simpler than the original statement.

  • @terry_willis
    @terry_willis 21 день тому

    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?

    • @dazartingstall6680
      @dazartingstall6680 21 день тому +1

      Because there's two unknowns in the equation. The area and the value of x.

    • @gavindeane3670
      @gavindeane3670 21 день тому +2

      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?

    • @dazartingstall6680
      @dazartingstall6680 21 день тому

      @@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.

    • @gavindeane3670
      @gavindeane3670 20 днів тому

      ​@@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.

    • @terry_willis
      @terry_willis 20 днів тому +1

      @@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. :)

  • @georgecattani7199
    @georgecattani7199 19 днів тому

    =2400 sqf

  • @roundtwo3321
    @roundtwo3321 21 день тому

    The square of (3x + 5).

  • @helenaamaral4659
    @helenaamaral4659 20 днів тому

    2

  • @elliotlambert3817
    @elliotlambert3817 21 день тому

    The area you come up with needs a value for X you have no value for the area so its not the answer.

    • @gavindeane3670
      @gavindeane3670 20 днів тому

      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.

  • @Cheryl-h1z
    @Cheryl-h1z 21 день тому

    15x squared