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pre calculus

A piece of wire 20 ft long is cut into two pieces so that sum of the squares of the length of each piece is 202 Sq ft. Find the length of each piece

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Anonymous

  1. Set x = length of one piece .
    The length of the second piece is 20 - x .
    x^2 + ( 20 - x )^2 = 202
    x^2 + 400 - 40x + x^2 = 202
    2x^2 - 40x + 400 = 202
    Subtract 202 from each side.
    2x^2 - 40x + 198 = 0
    Divide each side by 2
    x^2 - 20x + 99 = 0
    (x - 9)(x - 11) = 0
    So x = 9 or x = 11
    And we can see that our requirements
    are satisfied when the piece lengths are 9 and 11.

    Can someone check my work if I did it correct?

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    Anonymous

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