Question

A triangle has side lengths of left parenthesis, 8, x, plus, 10, right parenthesis(8x+10) centimeters, left parenthesis, 2, x, plus, 5, right parenthesis(2x+5) centimeters, and left parenthesis, 7, y, minus, 9, right parenthesis(7y−9) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer
Multiple Choice Answers
minus, 2, y, plus, 7, plus, 18, x−2y+7+18x
6, plus, 7, y, plus, 10, x6+7y+10x
15, minus, 2, y, plus, 10, x15−2y+10x
minus, 2, y, plus, 25, x−2y+25x

Answer 1

To find the perimeter of the triangle, we need to add the lengths of all three sides together. The side lengths are given as:

1. \( 8x + 10 \) cm
2. \( 2x + 5 \) cm
3. \( 7y - 9 \) cm

Now let's add these three expressions together to find the perimeter:

\[
P = (8x + 10) + (2x + 5) + (7y - 9)
\]

Combining like terms, we will first add the coefficients of \(x\), then the constants, and finally the \(y\) term:

1. Combine the \(x\) terms:
\[
8x + 2x = 10x
\]

2. Combine the constant terms:
\[
10 + 5 - 9 = 6
\]

3. The \(y\) term remains as is:
\[
7y
\]

Now, putting it all together, we have:
\[
P = 10x + 7y + 6
\]

So the expression that represents the perimeter of the triangle is:
\[
\boxed{10x + 7y + 6}
\]

In your multiple-choice options, the closest match is:
- \(6 + 7y + 10x\)

Thus, selecting this option would represent the correct perimeter of the triangle.