Question

A triangle has side lengths of left parenthesis, 8, f, plus, g, right parenthesis(8f+g) centimeters, left parenthesis, 4, f, minus, 5, h, right parenthesis(4f−5h) centimeters, and left parenthesis, 9, h, plus, 7, g, right parenthesis(9h+7g) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answer 1

To find the perimeter of a triangle, we sum the lengths of its sides. The side lengths of the triangle are given as:

1. \(8f + g\) centimeters
2. \(4f - 5h\) centimeters
3. \(9h + 7g\) centimeters

The perimeter \(P\) of the triangle can be expressed as:

\[
P = (8f + g) + (4f - 5h) + (9h + 7g)
\]

Now, we can combine the like terms:

1. Combine the \(f\) terms:
- \(8f + 4f = 12f\)

2. Combine the \(g\) terms:
- \(g + 7g = 8g\)

3. Combine the \(h\) terms:
- \(-5h + 9h = 4h\)

Now, putting it all together, we have:

\[
P = 12f + 8g + 4h
\]

Thus, the expression representing the perimeter of the triangle is:

\[
\boxed{12f + 8g + 4h}
\]