The rectangular floor of a closet is divided into two right triangles by drawing a diagonal. One leg of the right triangle is 11 foot less than twicethan twice the other leg. The hypotenuse is 17 feet. Determine the closet's length and width. Let the width be the shorter side.

Question

Lorenzo

Mathematics

6 December, 04:51

The rectangular floor of a closet is divided into two right triangles by drawing a diagonal. One leg of the right triangle is 11 foot less than twicethan twice the other leg. The hypotenuse is 17 feet. Determine the closet's length and width. Let the width be the shorter side.

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Lillie Adkins · Answer 1

W = width

2w + 2 = length

w^2 + (2w + 2) ^2 = 13^2

w^2 + 4w^2 + 8w + 4 - 169 = 0

5w^2 + 8w - 165 = 0

(5w + 33) (w - 5) = 0

w = 5 ft width

2 (5) + 2 = 12 ft length