Question

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.
e) if x = 4, triangle 1 has the greater perimeter.
f) if x = 5, triangle 2 has the greater perimeter.

Explanation:

Step1: Calculate perimeter of Triangle 1

Perimeter of Triangle 1: \(3x + 6+2(-2x + 16)\)

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Step2: Calculate perimeter of Triangle 2

Perimeter of Triangle 2: \(3x+8 + 2(5x-14)\)

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Step3: Check option E

When \(x = 4\)
Perimeter of Triangle 1: \(-4 + 38=34\)
Perimeter of Triangle 2: \(13\times4-20=52 - 20=32\)
Since \(34>32\), Triangle 1 has greater perimeter when \(x = 4\)

Step4: Check option F

When \(x = 5\)
Perimeter of Triangle 1: \(-5+38 = 33\)
Perimeter of Triangle 2: \(13\times5-20=65 - 20=45\)
Since \(45>33\), Triangle 2 has greater perimeter when \(x = 5\)

Answer:

B. The perimeter of Triangle1 is \(-x + 38\), C. The perimeter of Triangle 2 is \(13x-20\), E. If \(x = 4\), Triangle 1 has the greater perimeter, F. If \(x = 5\), Triangle 2 has the greater perimeter.