Question

A rectangular sandbox is surrounded on all sides by a strip of grass that is 5 ft wide on all sides. The length of the sandbox is 4 ft more then width, and the total area for the sandbox and the grass is 189 square feet. Find the dimensions of the sandbox.

Answer 1

Dimensions:

Length = 13.256m

width = 9.256m

Explanation:

Let the length of the sandbox be = l and its width be = w

The length of the sandbox is 4 ft more than the width.

This means that
`l = 4 + w` ----- equation 1

For the next step, we will be assuming that the strip of grass is a perfect rectangle. The length of the grass strip will be equals to the length of the sandbox.

Area of the grass = length X width =
`(4 +w) * 5= 5(4+w)`------ equation 2

The total area for the sandbox and the grass is 189 square feet.

This means that

`(w * (4+w)) + 5(4+w)=189\\w^2+4w+20+5w=189\\w^2+9w-169=0\\w=9.256m`

(Kindly note that the positive value for the width was chosen as length cannot be negative).

Now that we have our width, we can put this into equation 1 to get the length.

`l=9.256+4=13.256m`