Question

1. the length of a rectangle is eight more than twice its width. the perimeter is 88 feet. find the dimensions of the rectangle. variable: __________ equation: ________ solution: __________

Explanation:

Step1: Define the variable

Let the width of the rectangle be $w$. Then the length $l = 2w + 8$.

Step2: Write the perimeter - formula equation

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 88$, we substitute $l$ and $P$ into the formula: $88=2((2w + 8)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $88=2(3w + 8)$. Then distribute the 2: $88 = 6w+16$.

Step4: Solve for $w$

Subtract 16 from both sides: $88−16=6w$, so $72 = 6w$. Divide both sides by 6: $w = 12$.

Step5: Find the length $l$

Substitute $w = 12$ into the length formula $l=2w + 8$. Then $l=2\times12 + 8=24 + 8=32$.

Answer:

Variable: Let $w$ be the width of the rectangle.
Equation: $88=2((2w + 8)+w)$
Solution: Width $w = 12$ feet, Length $l = 32$ feet.