Question

a triangle has side lengths of (6x + 10y) centimeters, (8x - 9z) centimeters, and (4z - 7y) centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
-5z + 3y + 14x
-3yz + 16xy - xz
14y + 14x - 16z
-6yz + 18xz

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is the sum of the lengths of its three sides. So $P=(6x + 10y)+(8x - 9z)+(4z - 7y)$.

Step2: Remove parentheses

$P = 6x+10y + 8x-9z + 4z-7y$.

Step3: Combine like - terms

Combine the $x$ - terms: $6x+8x=14x$; combine the $y$ - terms: $10y-7y = 3y$; combine the $z$ - terms: $-9z + 4z=-5z$. So $P=-5z + 3y+14x$.

Answer:

$-5z + 3y + 14x$