SOLUTION: The length of a rectangular graden is 5ft longer than its width. The garden is surrounded by a 2-foot-wide sidewalk. The sidewalk has an area of 76 sq ft. Find the dimensions of th

Algebra ->  Rectangles -> SOLUTION: The length of a rectangular graden is 5ft longer than its width. The garden is surrounded by a 2-foot-wide sidewalk. The sidewalk has an area of 76 sq ft. Find the dimensions of th      Log On


   

Question 188304: The length of a rectangular graden is 5ft longer than its width. The garden is surrounded by a 2-foot-wide sidewalk. The sidewalk has an area of 76 sq ft. Find the dimensions of the garden.
Answer by solver91311(24713) About Me  (Show Source):
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If the sidewalk is 2 ft wide all the way around, then the rectangle defined by the outer edge of the sidewalk is 4 feet longer and 4 feet wider than the garden. So let the width of the garden be x and then the length of the garden is x + 5, so the area of the garden is:



And the area of the rectangle defined by the outer edge of the sidewalk is:



And the difference between the two is 76 square feet, so:



Solve for x:





So the width of the garden is 5 feet, the length is 10 feet.

Check:







Answer checks.

John