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?

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Answer 1 · 2018-03-23T22:50:20

The area is $2160 f t^{2}$ $2160 ft^2$

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

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

$l + w = \frac{192}{2} \Rightarrow l + w = 96$ $l+w=192/2 rArr l+w=96$

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

$l : w = 5 : 3 \Rightarrow l = \frac{5}{3} w$ $l:w =5:3 rArr l=5/3w$

Let's plug that back into the equation:

$\frac{5}{3} w + w = 96 \Rightarrow \frac{8}{3} w = 96$ $5/3w+w=96 rArr 8/3w=96$

$w = \frac{3}{8} \times 96 \Rightarrow w = 36 f t$ $w=3/8xx96 rArr color(red)(w=36 ft)$

$l = \frac{5}{3} w = \frac{5}{3} \cdot 36 \Rightarrow l = 60 f t$ $l=5/3w=5/3*36 rArr color(blue)(l=60 ft)$

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

$A = l \times w$ $A=lxxw$

$A = 36 f t \cdot 60 f t$ $A=36ft*60ft$

$A = 2160 f t^{2}$ $color(green)(A=2160 ft^2)$