Question

1 - 36 if the perimeter of the rectangle at right is 112 cm, write an equation that represents this fact? then, solve for x. 4x + 3 2x - 7

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, $l=4x + 3$ and $w = 2x-7$, and $P = 112$. So the equation is $2((4x + 3)+(2x - 7))=112$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $(4x + 3)+(2x - 7)=4x+2x+3 - 7=6x - 4$. Then the equation becomes $2(6x - 4)=112$. Distribute the 2: $12x-8 = 112$.

Step3: Solve for x

Add 8 to both sides of the equation: $12x-8 + 8=112 + 8$, which gives $12x=120$. Divide both sides by 12: $x=\frac{120}{12}=10$.

Answer:

The equation is $2((4x + 3)+(2x - 7))=112$ and $x = 10$.