SOLUTION: If the width of a certain rectangle is increased by 28 and the length is reduced by 39, we get a square with the same area as the original rectangle. Find the length and width of t

Algebra ->  Rectangles -> SOLUTION: If the width of a certain rectangle is increased by 28 and the length is reduced by 39, we get a square with the same area as the original rectangle. Find the length and width of t      Log On


   

Question 950061: If the width of a certain rectangle is increased by 28 and the length is reduced by 39, we get a square with the same area as the original rectangle. Find the length and width of the original rectangle.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
W=original width; L=original length
W+28=L-39 Add 39 to each side
W+67=L
L*W=(W+28)(L-39) Substitute for L
(W+67)(W)=(W+28)((W+67)-39)
(W^2+67W)=(W+28)(W+28)
W^2+67W=W^2+56W+784 Subtract W^2+56W from each side.
11W=784 Divide each side by 11.
W=71.27 The original width was 71.27
L=W+67=138.27 The original length was 138.27
ANSWER The original rectangle was 138.27 units by 71.27 units.
CHECK
L-39=138.27-39=99.27=Length of side of square.
W+28=71.27+28=99.27=length of side of square.
Areas are equal
L*W=S*s
138.27*71.27=99.27*99.27
9854.5 sq units=9854.5 sq units