SOLUTION: If the opposite sides of a square are increased by 12 inches and the other two sides are decreased by 4 inches, a rectangle is formed having the same area. What are the dimensions

Algebra ->  Surface-area -> SOLUTION: If the opposite sides of a square are increased by 12 inches and the other two sides are decreased by 4 inches, a rectangle is formed having the same area. What are the dimensions       Log On


   

Question 437852: If the opposite sides of a square are increased by 12 inches and the other two sides are decreased by 4 inches, a rectangle is formed having the same area. What are the dimensions of each polygon?
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Let x inches the side of square. If we increase the side by 12 it becomes: x+12
If we decrease the side by 4 it becomes: x-4 inches.
The area of square was:x%5E2. The area of rectangle will be:%28x%2B12%29%28x-4%29
Since the rectangle and square have the same area, we write the equation:
x%5E2=%28x%2B12%29%28x-4%29, solve this equation: x%5E2=x%5E2%2B8x-48 => 8x=48 =>
x=6.
Answer:The side of square is 6 inches while the dimensions of rectangle are:
The length: 6+12=18 inches and the width: 6-4=2 inches.