Question

the perimeter of the rectangle below is 76 units. find the length of side $overline{rs}$. write your answer without variables.

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ and $w$ are the length and width. Here, $l=3x$ and $w = 2x + 3$, and $P=76$. So, $76=2(3x+(2x + 3))$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $3x+(2x + 3)=5x + 3$. Then the equation becomes $76 = 2(5x + 3)$. Distribute the 2: $76=10x+6$.

Step3: Solve for $x$

Subtract 6 from both sides of the equation: $76 - 6=10x$, so $70 = 10x$. Divide both sides by 10: $x = 7$.

Step4: Find the length of $RS$

Side $RS$ has length $3x$. Substitute $x = 7$ into $3x$. So, $RS=3\times7 = 21$.

Answer:

21