Math word problem

Question

The floor of a rectangular storage room is divided into two right triangles by drawing a diagonal. One leg of the resulting triangle, the width of the room, is 4 feet more that two times the other leg, the length of the room. The hypotenuse is 26 feet. Find the length and width of the room.

Answer 1

Draw a figure.

L - Length and 2L + 4 = W

Pythagorean theorem

$L^2+(2L+4{)}^2=26^2$

$4L^2+16L+16+L^2=676$

$5L^2+16L-660=0$

The quadratic formula gives an extraneous root and L = 10

W = 24