# 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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