We are given that a rectangular playground is surrounded by an 80-foot fence. In other words, the perimeter of this rectangular playground is 80 feet. Let's recall the formula for the perimeter of a rectangle.
P=2a+2b
In this formula, a and b are the side lengths of the rectangle. In our exercise we have that a shorter side of the playground is r and the longer side is 10 feet longer than r. We can substitute all this information into the perimeter formula. Let's substitute 80 for P, r for a, and r+ 10 for b.
80=2( r)+2( r+ 10)
⇕
2(r+10)+2r=80
After rearranging terms on the right-hand side and rearranging the equation, our solution corresponds with answer J.
