Question

the perimeter of the pentagon below is 67 units. find the length of side $overline{pq}$. write your answer without variables.

Explanation:

Step1: Set up perimeter equation

The perimeter of a pentagon is the sum of its side - lengths. So, $(3y - 1)+(y + 3)+11 + 2y+12=67$.

Step2: Combine like - terms

Combine the $y$ terms and the constant terms: $(3y+y + 2y)+(-1 + 3+11 + 12)=67$, which simplifies to $6y+25 = 67$.

Step3: Solve for $y$

Subtract 25 from both sides of the equation: $6y=67 - 25$, so $6y=42$. Then divide both sides by 6: $y=\frac{42}{6}=7$.

Step4: Find the length of side $PQ$

The length of side $PQ$ is $3y - 1$. Substitute $y = 7$ into the expression: $3\times7-1=21 - 1=20$.

Answer:

20