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?

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Answer 1 · 2016-12-30T10:23:12

$A = 1625$ $A = 1625$

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

$\Rightarrow l = 3 w - 10$ $=> l = 3w - 10$

$P = 2 l + 2 w$ $P = 2l + 2w$

$\Rightarrow 180 = 2 (3 w - 10) + 2 w$ $=> 180 = 2(3w - 10) + 2w$

$\Rightarrow 180 = 6 w - 20 + 2 w$ $=> 180 = 6w - 20 + 2w$

$\Rightarrow 200 = 8 w$ $=> 200 = 8w$

$\Rightarrow w = 25$ $=> w = 25$

$> l = 3 (25) - 10 = 65$ $> l = 3(25) - 10 = 65$

$A = l w$ $A = lw$

$\Rightarrow A = 65 \cdot 25$ $=> A = 65*25$

$\Rightarrow A = 1625$ $=> A = 1625$