SOLUTION: The length of a rectangle is 3m less than twice its width, and the area of the rectangle is 27m^2. Find the dimensions of the rectangle. Any help is greatly appreciated. Thank y

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is 3m less than twice its width, and the area of the rectangle is 27m^2. Find the dimensions of the rectangle. Any help is greatly appreciated. Thank y      Log On


   

Question 455939: The length of a rectangle is 3m less than twice its width, and the area of the rectangle is 27m^2. Find the dimensions of the rectangle.
Any help is greatly appreciated. Thank you.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the area of the rectangle is A=L%2AW

The length L is 3m less than twice its width W: L%2B3m=2W...->...L=2W-3m
A=L%2AW
27m%5E2=%282W-3m%29%2AW
27m%5E2=2W%5E2-3m%2AW
2W%5E2-3Wm-27m%5E2=0....use quadratic formula
W+=+%28-%28-3m%29+%2B-+sqrt%28+%28-3m%29%5E2-4%2A2%2A%28-27m%5E2%29+%29%29%2F%282%2A2%29+
W+=+%283m+%2B-+sqrt%28+9m%5E2%2B216m%5E2%29+%29%29%2F4+
W+=+%283m+%2B-+sqrt%28+225m%5E2%29+%29%29%2F4+
W+=+%283m+%2B-+15m+%29%29%2F4+...you need only positive root because width cannot be negative

W+=+%283m+%2B+15m+%29%2F4+
W+=+%2818m+%29%2F4+
W+=+4.5m++......now find the L

L=2%2A4.5m+-3m
L=9m+-3m
L=6m