Question

the length of a rectangular garden is 5 feet longer than its width. The garden is surrounded by a 2-foot-wide sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden.

Answer 1

he width is 5 feet and the length 10 feet 

Let the width of the garden = W 
Therefore the length = W + 5 

The two sidewalks alongside the length are therefore W + 5 feet long by 2 feet wide = 2(W + 5) square feet each 
The 2 sidewalks alongside the width = W feet long by 2 feet wide = 2W square feet each 
In addition there are the 4 corners which are each 2 feet by 2 feet = 4 square feet each 
Area of sidewalk is therefore 

2 * lengths = 2 * 2(W + 5) = 4W + 20 
2 * widths = 2 * 2W = 4W 
4 corners = 4 * 4 = 16 square feet 
But we are told that the area = 76 square feet 
Therefore 4W + 20 + 4W + 16 = 76 
8W + 36 = 76 
8W = 40 
W = 5 
Therefore as the width is five feet the length is 5 + 5 = 10 feet