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Math Help - quadratic problem - please get me started

  1. #1
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    quadratic problem - please get me started

    This is the question:
    A strand of wire of length 32cm is cut into two pieces. One piece is bent to form a rectangle of width x cm and length (x + 2) cm, and the other piece is bent to form a square.
    A) show that the square has sides of length (7 - x) cm.
    B) given that the total of the areas enclosed by both the rectangle and the square is 31cm2., form an equation for x and solve t to find the value of x.

    I can for example work out that:
    x^2 + 2x + 32-(x^2 + 2x)=32

    But the x's all cancel each other out so can't work out how to get x?

    Can someone give me a helping hand please?

    Angus
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  2. #2
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    Quote Originally Posted by angypangy View Post
    This is the question:
    A strand of wire of length 32cm is cut into two pieces. One piece is bent to form a rectangle of width x cm and length (x + 2) cm, and the other piece is bent to form a square.
    A) show that the square has sides of length (7 - x) cm.

    rectangle perimeter = 2[x + (x+2)] = 2x + 2(x+2) = 4x + 4

    square perimeter = 32 - (4x + 4) = 28 - 4x

    square side = (28 - 4x)/4 = 7 - x


    B) given that the total of the areas enclosed by both the rectangle and the square is 31cm2., form an equation for x and solve t to find the value of x.

    x(x+2) + (7-x)^2 = 31

    solve for x
    ...
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  3. #3
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    Quote Originally Posted by angypangy View Post
    This is the question:
    A strand of wire of length 32cm is cut into two pieces. One piece is bent to form a rectangle of width x cm and length (x + 2) cm, and the other piece is bent to form a square.
    A) show that the square has sides of length (7 - x) cm.
    B) given that the total of the areas enclosed by both the rectangle and the square is 31cm2., form an equation for x and solve t to find the value of x.

    I can for example work out that:
    x^2 + 2x + 32-(x^2 + 2x)=32

    But the x's all cancel each other out so can't work out how to get x?

    Can someone give me a helping hand please?

    Angus
    (a) Perimeter of the square = 32-2(x+2)-2x
    Length = (28-4x)/4

    (b)Area of square = (7-x)^2 and area of rectangle = x(x+2)

    (7-x)^2+(x+2)(x)=31

    2x^2-12x+18=0

    (x-3)^2=0

    x=3
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