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.
Accepted Solution
A:
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