SOLUTION: If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm squared. What were the dimensions of the original square?

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm squared. What were the dimensions of the original square?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 114255: If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm squared. What were the dimensions of the original square?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the original length of each side of the square.
The original area is then:
A+=+x%5E2
Decreasing the sides by 2 cm. (x-2) results in the area being decreased by 36 sq. cm. (A - 36), so you can write:
%28x-2%29%5E2+=+%28A-36%29 for the new area. Substitute A+=+x%5E2 and solve for x.
%28x-2%29%5E2+=+x%5E2-36 Simplify.
x%5E2-4x%2B4+=+x%5E2-36 Subtract x%5E2 from both sides.
-4x%2B4+=+-36 Subtract 4 from both sides.
-4x+=+-40 Divide both sides by -4.
x+=+10cm.