SOLUTION: If the sides of a square are decreased by 2cm, the area is decreased by 36m^. What were the dimensions of the original square? (x-6)(x+6) Am I on the right track with this?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If the sides of a square are decreased by 2cm, the area is decreased by 36m^. What were the dimensions of the original square? (x-6)(x+6) Am I on the right track with this?      Log On


   

Question 113087: If the sides of a square are decreased by 2cm, the area is decreased by 36m^. What were the dimensions of the original square?
(x-6)(x+6) Am I on the right track with this?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Are you sure the area is decreased by 36 square METERS? 36 sq centimeters would make more sense.

If it actually is 36m%5E2 like you say, then let x be the length of the side of the original square.

The area of the original square is then x%5E2. The area of the new square would then be x%5E2-36m%5E2. But since the length of the side of the new square is x-.02m, , the area of the new square is also %28x-.02m%29%5E2

We can now set these two expressions for the area of the new square to be equal.

x%5E2-36=%28x-.02%29%5E2
x%5E2-36=x%5E2-.04x%2B.0004, expand the binomial using FOIL
-36.0004=-.04x, collect terms
x=36.0004%2F.04=900.01, multiply by -1 and divide by .04

The answer is 900.01 meters.

The problem set up and the equations are the same if you really meant 36cm%5E2. The only thing that changes are the numbers.

x%5E2-36=%28x-2%29%5E2
x%5E2-36=x%5E2-4x%2B4, expand the binomial using FOIL
-40=-4x, collect terms
x=40%2F4=10, multiply by -1 and divide by 4

The answer is 10cm.

And to answer your question, no, %28x-6%29%28x%2B6%29 has nothing to do with this problem. That is the correct factorization of the x%5E2-36 expression for the area of the new square, but as you have seen factoring this expression wasn't necessary.

Hope that helps,
John