Question

1. if ab is 4x - 2, cb is 3x + 1 and the perimeter of the rectangle is 68, find x.
2. if m∠dpa

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ and $w$ are the length and width. Here, if $AB$ is the length and $CB$ is the width, then $P=2((4x - 2)+(3x + 1))$.

Step2: Simplify the expression inside the parentheses

$(4x - 2)+(3x + 1)=4x-2 + 3x+1=7x - 1$. So the perimeter formula becomes $P = 2(7x - 1)$.

Step3: Set up the equation using the given perimeter

Since $P = 68$, we have the equation $2(7x - 1)=68$.

Step4: Solve the equation for $x$

First, divide both sides of the equation by 2: $\frac{2(7x - 1)}{2}=\frac{68}{2}$, which gives $7x-1 = 34$. Then add 1 to both sides: $7x-1 + 1=34 + 1$, so $7x=35$. Finally, divide both sides by 7: $\frac{7x}{7}=\frac{35}{7}$, and $x = 5$.

Answer:

$x = 5$