SOLUTION: Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 6 more squa

Algebra ->  Rectangles -> SOLUTION: Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 6 more squa      Log On


   

Question 213483: Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 6 more square feet than the smaller. What is the width of the rectangles?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two rectangles have the same width.
let w = width of both rectangles
:
The length of one is 1 foot longer than the width.
L1 = w + 1
The length of the other is 2 feet longer than the width.
L2 = w + 2
;
The larger rectangle has 6 more square feet than the smaller.
W*L2 - W*L1 = 6
:
What is the width of the rectangles?
Replace L2 in the above equation with (W+2);
Replace L1 in the above equation with ((W+1)
W*(W+2) - W*(W+1) = 6
W^2 + 2W - W^2 - W = 6
2W - W = 6
W = 6 is the width of both rectangles
;
:
Check solution
8*6 - 7*6 = 6