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