SOLUTION: A square is altered so one of the sides is increased by 4 while the other side is decreased by 2. The area of the new rectangle is 55 square feet. Find the dimensions of the rectan

Algebra ->  Rectangles -> SOLUTION: A square is altered so one of the sides is increased by 4 while the other side is decreased by 2. The area of the new rectangle is 55 square feet. Find the dimensions of the rectan      Log On


   

Question 1042038: A square is altered so one of the sides is increased by 4 while the other side is decreased by 2. The area of the new rectangle is 55 square feet. Find the dimensions of the rectangle and the area of the original square.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A square is altered so one of the sides is increased by 4 while the other side is decreased by 2.
The area of the new rectangle is 55 square feet.
Find the dimensions of the rectangle and the area of the original square.
:
let s = the length of the side of the square
then
(s+4) = the length of the new rectangle
and
(s-2) = the width
"The area of the new rectangle is 55 square feet. "
(s+4)*
(s-2) = 55
FOIL
s^2 - 2s + 4s - 8 = 55
Combine to form a quadratic equation
s^2 + 2s - 8 - 55 = 0
s^2 + 2s - 63 = 0
Factors to
(s+9)(s-7) = 0
The positive solution is what we want here
s = 7 ft is the side of the square
the area of the square: 7^2 = 49 sq ft
therefore
7+4 = 11 ft the length of the rectangle
and
7-2 = 5 ft is the width
:
:Check this by finding the area of the new rectangle with these value
11 * 5 = 55