Question

consider the rectangle shown. if the perimeter of the rectangle is 52, what is the value of x? enter the answer in decimal form. 2x - 1 3x + 5

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is given by $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=3x + 5$ and $w = 2x-1$, and $P = 52$. So, $52=2((3x + 5)+(2x-1))$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $(3x + 5)+(2x-1)=3x+2x + 5 - 1=5x + 4$. Then the equation becomes $52=2(5x + 4)$. Distribute the 2: $52 = 10x+8$.

Step3: Solve for $x$

Subtract 8 from both sides of the equation: $52-8=10x$, so $44 = 10x$. Then divide both sides by 10: $x=\frac{44}{10}=4.4$.

Answer:

$4.4$