Question

write a simplified expression that represents the length of the perimeter of the shape below. find the perimeter of the quadrilateral

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a quadrilateral is the sum of the lengths of its four - sides. Let the side lengths be $a = 8n - 7$, $b = 4n+5$, $c = 8n - 7$, $d = 4n + 5$.

Step2: Write the sum expression

$P=(8n - 7)+(4n + 5)+(8n - 7)+(4n + 5)$

Step3: Combine like - terms

First, combine the $n$ terms: $8n+4n + 8n+4n=(8 + 4+8 + 4)n=24n$.
Then, combine the constant terms: $-7 + 5-7 + 5=(-7-7)+(5 + 5)=-14 + 10=-4$.
So, $P = 24n-4$.

Answer:

$24n - 4$