Question

The perimeter of the rectangular front lawn of the library is 192 feet. The ratio of the length to the width is 5:3. What is the area of the lawn?

Answer 1

The area is `2160 ft^2`

Explanation:

If the perimeter is 192, we can write the equation as such:

`l+l+w+w=2l+2w=2(l+w)=192`

`l+w=192/2 rArr l+w=96`

Additionally, we can solve for one of the two sides since we know the ratio:

`l:w =5:3 rArr l=5/3w`

Let's plug that back into the equation:

`5/3w+w=96 rArr 8/3w=96`

`w=3/8xx96 rArr color(red)(w=36 ft)`

`l=5/3w=5/3*36 rArr color(blue)(l=60 ft)`

Now that we know length and width, we can calculate area:

`A=lxxw`

`A=36ft*60ft`

`color(green)(A=2160 ft^2)`