Question

a triangle has side lengths of (5t + 5u) centimeters, (6v + 7t) centimeters, and (6v + 8u) centimeters. which expression represents the perimeter, in centimeters, of the triangle? the perimeter of a triangle is the sum of all of its sides: 5t + 5u + 7t + 6v + 6v + 8u 5t + 5u + 7t + 6v + 6v + 8u identify like terms 5t + 7t + 5u + 8u + 6v + 6v the commutative property allows us to rearrange the terms

Explanation:

Step1: Combine like - terms of \(t\)

\(5t+7t=(5 + 7)t=12t\)

Step2: Combine like - terms of \(u\)

\(5u+8u=(5 + 8)u = 13u\)

Step3: Combine like - terms of \(v\)

\(6v+6v=(6 + 6)v=12v\)

Step4: Write the perimeter expression

The perimeter is \(12t + 13u+12v\)

Answer:

\(12t + 13u + 12v\)