SOLUTION: Suppose that the length of a certain rectangle is 6 meters less than three times its width. The perimeter of the rectangle is 52 meters. Find the length and width of the rectangle.

Algebra ->  Finance -> SOLUTION: Suppose that the length of a certain rectangle is 6 meters less than three times its width. The perimeter of the rectangle is 52 meters. Find the length and width of the rectangle.      Log On


   

Question 885665: Suppose that the length of a certain rectangle is 6 meters less than three times its width. The perimeter of the rectangle is 52 meters. Find the length and width of the rectangle.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A Small Change: Suppose that the length L of a certain rectangle is k meters less than m times its width w. The perimeter of the rectangle is p meters. Find the length and width of the rectangle.

p might or might not be an even number.
CONSTANTS: m, k, p
UNKNOWNS: L and w
L=mw-k and 2w%2B2L=p

2w%2B2%28mw-k%29=p using substitution;
2w%2B2mw-2k=p
%282%2B2m%29w-2k=p
%282%2B2m%29w=p%2B2k
highlight%28w=%28p%2B2k%29%2F%282%2B2m%29%29
-
Rearrange the L equation, mw=L+k, w=(L+k)/m.
-
Substitute w into the perimeter equation:
2%28L%2Bk%29%2Fm%2B2L=p
2%28L%2Bk%29%2B2mL=mp
2L%2B2k%2B2mL=mp
2L%2B2mL=mp-2k
%282%2B2m%29L=mp-2k
highlight%28L=%28mp-2k%29%2F%282%2B2m%29%29