Question

the perimeter of the rectangle below is 118 units. find the length of side bc. write your answer without variables.

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. In rectangle $ABCD$, let $AB=x + 3$ and $AD = 2x+1$. Then $P=2((x + 3)+(2x + 1))$.

Step2: Simplify the perimeter - expression

First, simplify the expression inside the parentheses: $(x + 3)+(2x + 1)=x+2x+3 + 1=3x + 4$. Then $P = 2(3x + 4)=6x+8$.

Step3: Solve for $x$

Since $P = 118$, we set up the equation $6x+8 = 118$. Subtract 8 from both sides: $6x=118 - 8=110$. Then divide both sides by 6: $x=\frac{110}{6}=\frac{55}{3}$.

Step4: Find the length of $BC$

In a rectangle, $BC = AD=2x + 1$. Substitute $x=\frac{55}{3}$ into $2x + 1$: $2\times\frac{55}{3}+1=\frac{110}{3}+1=\frac{110 + 3}{3}=\frac{113}{3}$.

Answer:

$\frac{113}{3}$