Question

the perimeter of the rectangle below is 118 units. find the length of side $overline{vw}$. write your answer without variables.

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$. Here, $l=3y + 3$, $w = 2y+1$, and $P = 118$. So we have $118=2((3y + 3)+(2y + 1))$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $(3y + 3)+(2y + 1)=3y+2y + 3 + 1=5y+4$. Then the equation becomes $118 = 2(5y + 4)$. Distribute the 2: $118=10y+8$.

Step3: Solve for y

Subtract 8 from both sides of the equation: $118 - 8=10y+8 - 8$, which gives $110 = 10y$. Divide both sides by 10: $y=\frac{110}{10}=11$.

Step4: Find the length of side $\overline{VW}$

The length of side $\overline{VW}$ is $3y + 3$. Substitute $y = 11$ into the expression: $3\times11+3=33 + 3=36$.

Answer:

36