Question

Rectangular garden that is 10 feet longer than it is wide. A sidewalk that is 3 feet in width surrounds the garden. The total area of the sidewalk is 396 square feet. What are the dimensions of the garden?

Answer 1

Answer:

• 35 feet long
• 25 feet wide

Step-by-step explanation:

Let w represent the width of the garden. Then the width of the garden and walk together will be w+6. The length of the garden is described as w+10, so the length with the walk is w+16.

The difference in areas with and without the walk is 396 square feet:

  (w+6)(w+16) -(w)(w+10) = 396

  w² +22w +96 -(w² +10w) = 396 . . . . expand products

  12w = 300 . . . . . . collect terms, subtract 96

  w = 25 . . . . . . . . . divide by 12

The dimensions of the garden are 25 feet wide by 35 feet long.