Question

two triangles are shown.
triangle 1
17
4(-3x + 22)
6x
triangle 2
5x
24
3(5x - 18)
a. represent the perimeter of each triangle as an algebraic expression written in simplest form.
b. if x = 5, which triangle has a greater perimeter?
keyboard help

Explanation:

Step1: Calculate the perimeter of Triangle 1

The perimeter \(P_1\) of a triangle is the sum of its side - lengths.

$$
LATEXBLOCK0
$$

Step2: Calculate the perimeter of Triangle 2

The perimeter \(P_2\) of a triangle is the sum of its side - lengths.

$$
LATEXBLOCK1
$$

Step3: Substitute \(x = 5\) into \(P_1\)

When \(x = 5\), \(P_1=105-6\times5=105 - 30=75\)

Step4: Substitute \(x = 5\) into \(P_2\)

When \(x = 5\), \(P_2=-30+20\times5=-30 + 100 = 70\)

Answer:

a. The perimeter of Triangle 1 is \(P_1 = 105-6x\), and the perimeter of Triangle 2 is \(P_2=-30 + 20x\).
b. When \(x = 5\), Triangle 1 has a greater perimeter.