Question

a triangle has side lengths of (6.2v + 5.4w) centimeters, (5.2v - 6.7x) centimeters, and (2.1x - 5.3w) centimeters. which expression represents the perimeter, in centimeters, of the triangle? answer -1.5vx + 11.6vw - 3.2wx -4.6x + 11.4v + 0.1w 11.4v + 7.5w - 12x 13.5vx - 6.6wx

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is the sum of the lengths of its sides. So $P=(6.2v + 5.4w)+(5.2v-6.7x)+(2.1x - 5.3w)$.

Step2: Remove parentheses

$P = 6.2v+5.4w + 5.2v-6.7x+2.1x - 5.3w$.

Step3: Combine like - terms

Combine the $v$ - terms: $6.2v+5.2v=(6.2 + 5.2)v=11.4v$.
Combine the $w$ - terms: $5.4w-5.3w=(5.4 - 5.3)w = 0.1w$.
Combine the $x$ - terms: $-6.7x+2.1x=(-6.7 + 2.1)x=-4.6x$.
So $P=-4.6x + 11.4v+0.1w$.

Answer:

$-4.6x + 11.4v+0.1w$