Question

the perimeter of the rectangle below is 106 units. find the length of side $overline{wx}$. write your answer without variables.

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$. Here, $l=3y$ and $w = 2y + 3$, and $P=106$. So $106=2(3y+(2y + 3))$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $3y+(2y + 3)=5y + 3$. Then the equation becomes $106 = 2(5y+3)$. Distribute the 2: $106=10y + 6$.

Step3: Solve for y

Subtract 6 from both sides of the equation: $106-6=10y$, so $100 = 10y$. Divide both sides by 10: $y = 10$.

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

The length of side $\overline{WX}=2y + 3$. Substitute $y = 10$ into the expression: $2\times10+3=20 + 3=23$.

Answer:

23