SOLUTION: A man has a square garden area with a sidewalk 2 feet wide all around it. If the area of the sidewalk plus garden is 196 square feet, what are the dimensions of the garden area?

Algebra ->  Geometry-proofs -> SOLUTION: A man has a square garden area with a sidewalk 2 feet wide all around it. If the area of the sidewalk plus garden is 196 square feet, what are the dimensions of the garden area?      Log On


   

Question 54442: A man has a square garden area with a sidewalk 2 feet wide all around it. If the area of the sidewalk plus garden is 196 square feet, what are the dimensions of the garden area?
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
First notice that they said that the garden was a square. That tells us that all of the sides are equal. The area of a square is highlight%28A=s%5E2%29
Let the side of the garden =x
If you were to draw a square with a bigger square extended 2 feet around it, you would see that the bigger square has sides that look like this:
2ft------x-------2ft, so s=2+x+2=x+4 is the side of the bigger square.
The area of the garden and the sidewalk can be found by finding the area of the big square, they told us that was: 196
Your problem to solve is:
A=s%5E2
196=%28x%2B4%29%5E2
+ or -sqrt%28196%29=sqrt%28%28x%2B4%29%5E2%29 (We can ignore the -sqrt%28196%29 because that would give you a - dimension.)
14=x%2B4
14-4=x%2B4-4
10=x
x was the side of the garden, so the dimensions of the garden would be: highlight%2810+ft+X+10+ft%29
Happy Calculating!!!