Question

the perimeter of the triangle below is 79 units. find the length of side \\(\overline{qr}\\). write your answer without variables. triangle image with vertices p, q, r; sides: pr = 4z, rq = z + 2, pq = 5z - 3 \\(qr = \square\\)

Explanation:

Step1: Recall perimeter formula

The perimeter of a triangle is the sum of its three sides. So, \( 4z + (z + 2) + (5z - 3) = 79 \).

Step2: Simplify the left side

Combine like terms: \( 4z + z + 5z + 2 - 3 = 10z - 1 \). So the equation is \( 10z - 1 = 79 \).

Step3: Solve for z

Add 1 to both sides: \( 10z = 79 + 1 = 80 \). Then divide by 10: \( z = \frac{80}{10} = 8 \).

Step4: Find length of QR

QR is \( z + 2 \). Substitute \( z = 8 \): \( 8 + 2 = 10 \).

Answer:

10