# A rectangular park has a length that is 10 less than three times its width. Given the perimeter of the park is 180 feet, how do you find the area?

Dec 30, 2016

$A = 1625$

#### Explanation:

Let $w$ be the width of the park
Let $l$ be the length of the park

$\implies l = 3 w - 10$

$P = 2 l + 2 w$

$\implies 180 = 2 \left(3 w - 10\right) + 2 w$

$\implies 180 = 6 w - 20 + 2 w$

$\implies 200 = 8 w$

$\implies w = 25$

$> l = 3 \left(25\right) - 10 = 65$

$A = l w$

$\implies A = 65 \cdot 25$

$\implies A = 1625$