Question

a triangle has side lengths of (9f + g) centimeters, (5f + 9h) centimeters, and (2h + 7g) centimeters. which expression represents the perimeter, in centimeters, of the triangle? answer 8g + 11h + 14f 16fh + 17gh 9h + 14f + 10g 14fh + 9gh + 10fg

Explanation:

Step1: Recall perimeter formula

The perimeter \(P\) of a triangle is the sum of its side - lengths. So \(P=(9f + g)+(5f + 9h)+(2h + 7g)\).

Step2: Remove parentheses

\(P = 9f+g + 5f+9h+2h + 7g\).

Step3: Combine like - terms

For the \(f\) terms: \(9f+5f = 14f\); for the \(g\) terms: \(g + 7g=8g\); for the \(h\) terms: \(9h+2h = 11h\). So \(P=14f + 8g+11h\).

Answer:

A. \(8g + 11h+14f\)