Question

the side lengths of two triangles are shown.which of the following statements are true? select all that apply.a) the perimeter of triangle 1 is $x + 22$.b) the perimeter of triangle 1 is $-x + 38$.c) the perimeter of triangle 2 is $13x - 20$.d) the perimeter of triangle 2 is $8x - 6$.

Explanation:

Step1: Calculate perimeter of Triangle 1

Perimeter of a triangle is sum of side - lengths.
For Triangle 1, side - lengths are \(3x\), \(6\), and \(2(-2x + 16)\).
First, simplify \(2(-2x + 16)=-4x + 32\).
Then, perimeter \(P_1=3x+6+(-4x + 32)\).
Combine like terms: \(P_1=(3x-4x)+(6 + 32)=-x + 38\).

Step2: Calculate perimeter of Triangle 2

For Triangle 2, side - lengths are \(3x\), \(8\), and \(2(5x - 14)\).
First, simplify \(2(5x - 14)=10x-28\).
Then, perimeter \(P_2=3x + 8+(10x-28)\).
Combine like terms: \(P_2=(3x + 10x)+(8-28)=13x-20\).

Answer:

B) The perimeter of Triangle 1 is \(-x + 38\); C) The perimeter of Triangle 2 is \(13x - 20\)