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?

1 Answer
Mar 23, 2018

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)#