math

The diagonal of a rectangular room is 13 ft long. One wall measures 7 ft longer than the adjacent wall. Find the dimensions of the room.

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  1. x^2 + (x+7)^2 = 13^2
    So just solve for x and x+7

    Or, save yourself some time and remember the 5-12-13 Pythagorean triple.

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    oobleck
  2. The diagonal form a right triangle with the adjacent sides:
    x^2 + (x+7)^2 = 13^2
    x^2 + x^2+14x+49 = 169
    2x^2+14x-120 = 0
    x^2+7x-60 = 0. -60 = -5*12. -5+12 = 7 = B.
    (x-5)(x+12) = 0
    x-5 - 0. X = 5.
    x+12 = 0. X = -12.
    X = 5 ft.
    x+7 = 5+7 = 12 ft.
    Dimensions = 5ft. by 7ft.

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