Question

the perimeter of the rectangle below is 130 units. find the length of side $overline{ab}$. write your answer without variables. $ab = 38$

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ and $w$ are length and width. Here, $l=4x + 2$, $w = 3x$, and $P=130$. So, $130=2((4x + 2)+3x)$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $130 = 2(7x + 2)$. Then distribute the 2: $130=14x + 4$.

Step3: Solve for x

Subtract 4 from both sides: $130 - 4=14x$, so $126 = 14x$. Divide both sides by 14: $x=\frac{126}{14}=9$.

Step4: Find length of AB

Side $AB$ has length $4x + 2$. Substitute $x = 9$ into the expression: $4\times9+2=36 + 2=38$.

Answer:

$38$