SOLUTION: The length of a rectangular floor is 1m less than twice its width. if a diagnol of the rectangle is 17m, find the length and width of the floor.

Algebra ->  Pythagorean-theorem -> SOLUTION: The length of a rectangular floor is 1m less than twice its width. if a diagnol of the rectangle is 17m, find the length and width of the floor.       Log On


   

Question 236398: The length of a rectangular floor is 1m less than twice its width. if a diagnol of the rectangle is 17m, find the length and width of the floor.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let L = the length of the rectangle and W = its width.
L+=+2W-1 "The length (L) of a rectangle is 1m less than twice its width (W)."
From the Pythagorean theorem,...
sqrt%28L%5E2%2BW%5E2%29+=+17 "...a diagonal of the rectangle is 17m,..."
%28sqrt%28L%5E2%2BW%5E2%29%29%5E2+=+17%5E2 Simplify.
L%5E2%2BW%5E2+=+289 Substitute L+=+2W-1 ansd solve for W.
%282W-1%29%5E2%2BW%5E2+=+289
%284W%5E2-4W%2B1%29%2BW%5E2+=+289 Simplify and subtract 289 from both sides.
5W%5E2-4W-288+=+0 Solve using the quadratic formula:W+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a where: a = 5, b = -4 and c = -288.
W+=+%28-%28-4%29%2B-sqrt%28%28-4%29%5E2-4%285%29%28-288%29%29%29%2F2%284%29
W+=+%284%2B-sqrt%2816-%28-5760%29%29%29%2F8
W+=+%284%2B-sqrt%285776%29%29%2F8
highlight%28W+=+8%29 or cross%28W+=+-7.2%29 Discard the negative solution.
L+=+2W-1
L+=+2%288%29-1
L+=+15
The length is 15 meters and the width is 8 meters.