Question

a triangle has side lengths of $(9v - 7w)$ centimeters, $(7v + 10x)$ centimeters, and $(8x + 5w)$ centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
attempt 1 out of 2
$15x + 16v + w$
$2vw + 17vx + 13wx$
$18x - 2w + 16v$
$8wx + 24vx$
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Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is the sum of the lengths of its sides. So $P=(9v - 7w)+(7v + 10x)+(8x + 5w)$.

Step2: Remove parentheses

$P = 9v-7w + 7v+10x+8x + 5w$.

Step3: Combine like - terms

Combine the $v$ terms: $9v+7v = 16v$. Combine the $w$ terms: $-7w + 5w=-2w$. Combine the $x$ terms: $10x+8x = 18x$. So $P=18x-2w + 16v$.

Answer:

$18x - 2w+16v$ (corresponds to the third option in the multiple - choice list)