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
$11.5 - 0.5t + 0.9u$ $-14.4 + 16.6t + 9.7u$ $0.9u + 16.6t - 5.6$ $0.9u + 11t$

Explanation:

Step1: Recall the formula for the perimeter of a triangle

The perimeter \(P\) of a triangle is the sum of its side - lengths. If the side - lengths are \(a=(8.2t - 8.7)\), \(b=(8.4t + 3.1)\), and \(c=(9.7u - 8.8)\), then \(P=a + b + c\).

$$P=(8.2t - 8.7)+(8.4t + 3.1)+(9.7u - 8.8)$$

Step2: Remove the parentheses

$$P = 8.2t-8.7 + 8.4t+3.1+9.7u - 8.8$$

Step3: Group like terms

Group the \(t\) - terms (\(8.2t\) and \(8.4t\)), the constant terms (\(-8.7\), \(3.1\), and \(-8.8\)), and the \(u\) - term (\(9.7u\)):

$$P=(8.2t + 8.4t)+9.7u+(-8.7 + 3.1-8.8)$$

Step4: Combine like terms

For the \(t\) - terms: \(8.2t+8.4t=(8.2 + 8.4)t=16.6t\).
For the constant terms: \(-8.7+3.1-8.8=-8.7+(3.1-8.8)=-8.7 - 5.7=-14.4\).
The \(u\) - term remains \(9.7u\).

So, \(P=-14.4 + 16.6t+9.7u\)

Answer:

\(-14.4 + 16.6t + 9.7u\)