Question

the perimeter of the triangle below is 42 units. find the length of side $overline{vw}$. write your answer without variables. triangle with vertices v, w, x. sides: vx is 4z, vw is 3z - 1, wx is z + 3. then a box for vw =

Explanation:

Step1: Recall perimeter formula

The perimeter of a triangle is the sum of its three sides. So, \( 4z + (z + 3) + (3z - 1) = 42 \).

Step2: Simplify the left side

Combine like terms: \( 4z + z + 3 + 3z - 1 = (4z + z + 3z) + (3 - 1) = 8z + 2 \).

Step3: Solve for z

Set up the equation \( 8z + 2 = 42 \). Subtract 2 from both sides: \( 8z = 42 - 2 = 40 \). Then divide by 8: \( z = \frac{40}{8} = 5 \).

Step4: Find length of VW

The length of \( \overline{VW} \) is \( 3z - 1 \). Substitute \( z = 5 \): \( 3(5) - 1 = 15 - 1 = 14 \).

Answer:

14