Math word problem

Question

A rectangular park measuring 26yards by 31 yards is surrounded by a trail of uniform width. If the area of the park and the trail combined is 1800 square yards, what is the width of the path?

Answer 1

Make a figure and call x the width of the path.

The length and width of the combined rectangle are (31 + 2x) and (26 + 2x) respectively.

The area of this rectangle is (31 + 2x)(26 + 2x) = 1800

Expand this expression and collect terms to get:

$4x^2+114x-994=0$

The quadratic formula gives and extraneous root and x = 7.

You should put this answer back into the original problemt to be sure it is correct.