Question

a triangle has side lengths of (9v − 7w) centimeters, (7v + 10x) centimeters, and (8x + 5w) centimeters. which expression represents the perimeter, in centimeters, of the triangle? answer ○ 15x + 16v + w ○ 2vw + 17vx + 13wx ○ 18x − 2w + 16v ○ 8wx + 24vx

Explanation:

Step1: Recall perimeter formula

The perimeter \( P \) of a triangle is the sum of its three sides. So, \( P=(9v - 7w)+(7v + 10x)+(8x + 5w) \).

Step2: Combine like terms for \( v \)

For the terms with \( v \): \( 9v+7v = 16v \).

Step3: Combine like terms for \( w \)

For the terms with \( w \): \( - 7w+5w=-2w \).

Step4: Combine like terms for \( x \)

For the terms with \( x \): \( 10x + 8x=18x \).

Step5: Combine all terms

Putting it all together, the perimeter \( P = 18x-2w + 16v \).

Answer:

\( 18x - 2w + 16v \) (corresponding to the option "18x − 2w + 16v")