Question

the width of a rectangle is 8y - 4.5 feet and the length is 4.5y + 9 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 the formula for the perimeter of a rectangle

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

Step2: Substitute the given expressions for length and width into the formula

Given \(w=8y - 4.5\) and \(l = 4.5y+9\). Then \(P=2((4.5y + 9)+(8y - 4.5))\).

Step3: Simplify the expression inside the parentheses

\((4.5y + 9)+(8y - 4.5)=4.5y+8y+9 - 4.5=(4.5 + 8)y+(9 - 4.5)=12.5y + 4.5\).

Step4: Multiply by 2

\(P = 2(12.5y+4.5)=2\times12.5y+2\times4.5 = 25y+9\).

Answer:

\(25y + 9\)