The length of a rectangular floor is 1 meter less than twice its width. if a diagonal of the rectangle is 17 meters, find the length and width of the floor.

Givens
W = W
L = 2*W - 1
L^2 + W^2 = D^2
D = 17

Equation
(2W - 1)^2 + W^2 = D^2

Substitute and Solve
4W^2 - 4W + 1 + W^2 = 17^2
4W^2 - 4W + 1  + W^2 = 289 Collect like terms on the left.
5W^2 - 4W + 1 = 289 Subtract 289 from both sides.
5W^2 - 4W - 288 = 0 Now the tough part. Factor.
(5W + 36 )(W -  8     ) = 0

The first term has absolutely no meaning. You cannot have a negative floor dimension.

Find the Length and Width
W = 8
L = 2W - 1
L = 2*8 - 1
L = 16 - `1
L = 15

Check
a^2 + b^2 = c^2
8^2 + 15^2 = 17^2
64 + 225 = ? 289
289 = ! 289 They check.

Answer
L = 15
W = 8