Question

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.

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