Question

the width of a rectangle is 6y - 9.5 feet and the length is 9.5y + 10 feet. find the perimeter of the rectangle. the perimeter of the rectangle is feet (simplify your answer. use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.

Step2: Substitute length and width

Substitute $l=9.5y + 10$ and $w = 6y-9.5$ into the formula: $P=2((9.5y + 10)+(6y - 9.5))$.

Step3: Simplify inside parentheses

First, simplify the expression inside the parentheses: $(9.5y+10)+(6y - 9.5)=9.5y+6y+10 - 9.5=15.5y + 0.5$.

Step4: Multiply by 2

Then multiply the result by 2: $P=2(15.5y + 0.5)=2\times15.5y+2\times0.5 = 31y+1$.

Answer:

$31y + 1$