algebra

a wire of 16 inches cut into 2 pieces.
Each piece bent into a square.
Find the length of the two pieces so the sum of the areas of the two squares in 10 square inches.

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  1. L = Length of a wire

    x = Length of the first pice

    y = Length of the cecond pice

    x / 4 = Length of the first square

    y / 4 = Length of the second square

    L = 16 in

    16 = x + y

    y = 16 - x

    Area of the first pice = ( x / 4 ) ^ 2

    Area of the second pice = ( y / 4 ) ^ 2

    ( x / 4 ) ^ 2 + ( y / 4 ) ^ 2 = 10

    x ^ 2 / 16 + y ^ 2 / 16 = 10

    ( x ^ 2 + y ^ 2 ) / 16 = 10 Multiply both sides with 16

    x ^ 2 + y ^ 2 = 160

    x ^ 2 + ( 16 - x ) ^ 2 = 160

    ( Remark: ( 16 - x ) ^ 2 = 16 ^ 2 - 32 x + x ^ 2

    x ^ 2 + 16 ^ 2 - 32 x + x ^ 2 = 160

    2 x ^ 2 + 256 - 32 x = 160

    2 x ^ 2 + 256 - 160 - 32 x = 0

    2 x ^ 2 + 96 - 32 x = 0

    2 x ^ 2 - 32 x + 96 = 0 Divide both sides with 2

    x ^ 2 - 16 x + 48 = 0

    The exact solutions are:

    x = 12

    and

    x = 4

    Length of a wire = 16 in

    y = 16 - x

    When: x = 12 ; y = 16 - 12 = 4

    When x = 4 ; y = 16 - 4 = 12

    Length of the two pieces :

    12 in

    and

    4 in

    Proof:

    ( 12 / 4 ) ^ 2 + ( 4 / 4 ) ^ 2 = 10

    3 ^ 2 + 1 ^ 2 = 10

    9 + 1 = 10 in ^ 2

    P.S.

    If you don know how to solve equation:

    x ^ 2 - 16 x + 48 = 0

    In google type:

    quadratic equation online

    When you see list of results click on:
    Free Online Quadratic Equation Solver:Solve by Quadratic Formula

    When page be open in rectangle type:

    x ^ 2 - 16 x + 48 = 0

    and click option:
    solve it!

    You wil see solution step-by-step

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