Question

the perimeter of the pentagon below is 67 units. find the length of side \\( \overline{vw} \\).
write your answer without variables.
(image of a pentagon with vertices z, y, x, w, v. side zy is 3z, yx is 12, xw is z + 1, wv is 2z + 2, vz is 10. there is a box for vw = )

Explanation:

Step1: Set up the equation for perimeter

The perimeter of a pentagon is the sum of all its side lengths. So, \(10+(2z + 2)+(z + 1)+12+3z=67\).
Simplify the left - hand side: \((10 + 2+1+12)+(2z+z + 3z)=67\), which is \(25 + 6z=67\).

Step2: Solve for \(z\)

Subtract 25 from both sides: \(6z=67 - 25\), so \(6z=42\).
Divide both sides by 6: \(z=\frac{42}{6}=7\).

Step3: Find the length of \(VW\)

Since \(VW = 2z+2\), substitute \(z = 7\) into the expression. \(VW=2\times7+2=14 + 2=16\).

Answer:

\(16\)