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