Question

a triangle has side lengths of (8.2t - 8.7) centimeters, (8.4t + 3.1) centimeters, and (9.7u - 8.8) centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer:
11.5 - 0.3t - 0.9u -14.4 + 16.6t + 9.7u
0.9u + 16.6t - 5.6 0.9u + 11t

Explanation:

Step1: Recall perimeter formula

Perimeter of a triangle is the sum of its three sides. So we need to add \((8.2t - 8.7)\), \((8.4t + 3.1)\), and \((9.7u - 8.8)\).

Step2: Combine like terms for \(t\)

For the \(t\) terms: \(8.2t + 8.4t = (8.2 + 8.4)t = 16.6t\)

Step3: Combine constant terms

For the constant terms: \(-8.7 + 3.1 - 8.8 = (-8.7 - 8.8) + 3.1 = -17.5 + 3.1 = -14.4\)

Step4: Include the \(u\) term

The \(u\) term is \(9.7u\) (since there's only one \(u\) term). So combining all, we get \(-14.4 + 16.6t + 9.7u\) or \( -14.4 + 16.6t + 9.7u\) (which can be reordered as \( -14.4 + 16.6t + 9.7u\) matching one of the options).

Answer:

\(-14.4 + 16.6t + 9.7u\) (corresponding to the option with this expression)