SOLUTION: If a rectangle has an perimeter of 56 inches. What is the area of the width is one third of the length

Algebra ->  Rectangles -> SOLUTION: If a rectangle has an perimeter of 56 inches. What is the area of the width is one third of the length      Log On


   

Question 960068: If a rectangle has an perimeter of 56 inches. What is the area of the width is one third of the length
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let the length be L and the width W
we know that a perimeter is
P=2%28L%2BW%29
if a rectangle has an perimeter of 56in, then
56in=2%28L%2BW%29
56in%2F2=L%2BW
28in=L%2BW........solve for W
W=28in-L.....eq.1
if the width is one third of the length, then W=%281%2F3%29L
substitute it in W=28in-L.....eq.1
%281%2F3%29L=28in-L.......solve for L
3%281%2F3%29L=3%2A28in-3%2AL
L=84in-3L
L%2B3L=84in
4L=84in
L=84in%2F4
highlight%28L=21in%29
now find W
W=28in-L
W=28in-21in
highlight%28W=7in%29
then, the area will be:
A=L%2AW
A=21in%2A7in
highlight%28A=147in%5E2%29