SOLUTION: If two opposite sides of a square are increased by 15 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 75 square meters. Find the a

Algebra ->  Rectangles -> SOLUTION: If two opposite sides of a square are increased by 15 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 75 square meters. Find the a      Log On


   

Question 988688: If two opposite sides of a square are increased by 15 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 75 square meters. Find the area of the original square.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If two opposite sides of a square are increased by 15 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 75 square meters.
Find the area of the original square.
:
let x = the side of the original square
then
(x+15) = one pair of sides
and
(x-7) = the other pair of sides
:
The area equation
(x+15)*(x-7) = 75
FOIL
x^2 - 7x + 15x - 105 = 75
x^2 + 8x - 105 - 75 = 0
A quadratic equation
x^2 + 8x - 180 = 0
Factor easily to
(x+18)(x-10) = 0
the positive solution
x = 10 m, side of the original square
then
10^2 = 100 sq/m the area of the original square