Question

a triangle has side lengths of (2t - 4) centimeters, (7t - 2) centimeters, and (2u + 7) centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
3t + 9u
9t - 6 + 9u
9t + 2u + 1
9u + 5 - 2t

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is the sum of the lengths of its sides. So $P=(2t - 4)+(7t - 2)+(2u + 7)$.

Step2: Remove parentheses

$P = 2t-4 + 7t-2+2u + 7$.

Step3: Combine like - terms

Combine the $t$ - terms: $2t+7t = 9t$. Combine the constant terms: $-4-2 + 7=1$.
So $P=9t + 2u+1$.

Answer:

$9t + 2u + 1$