Question

the perimeter of the triangle below is 45 units. find the length of side \\( \overline { v x } \\).
write your answer without variables.

Explanation:

Step1: Set up the perimeter equation

The perimeter of a triangle is the sum of its sides. So, \(4z+(3z + 3)+(z + 2)=45\).
Simplify the left - hand side: \((4z+3z+z)+(3 + 2)=45\), which gives \(8z+5 = 45\).

Step2: Solve for \(z\)

Subtract 5 from both sides: \(8z=45 - 5\), so \(8z=40\).
Divide both sides by 8: \(z=\frac{40}{8}=5\).

Step3: Find the length of \(VX\)

Since \(VX = 4z\), substitute \(z = 5\) into the expression. So, \(VX=4\times5\).

Answer:

\(20\)