Expressions and Equations

Question

A rectangular park 40 yards wide was redesigned, and a path 1 yard wide was built around it. How long was the park before if, after the path was built, its area became 4200 square yards?

 

Answer 1

The original dimensions of the park are

 

L x W

 

The dimensions of the part with a 1 yard path around it are

 

(L+2) x (W+2)

We add 2 to the length and width because there will be a 1 yard path on all 4 sides.

 

The new area is 4200; the original width is 40.

 

Since Area = LW

4200 = (L+2)(W+2)

4200 = (L+2)(40+2) = (L+2)(42)

4200 = 42L + 84

4116 = 42L

L = 98 yards