Question

the width of a rectangle is 7y - 5.5 feet and the length is 5.5y + 7 feet. find the perimeter of the rectangle.

the perimeter of the rectangle is \\(\square\\) feet.
(simplify your answer. use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Recall Perimeter Formula

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \).

Step2: Substitute Length and Width

Given width \( w = 7y - 5.5 \) and length \( l = 5.5y + 7 \). Substitute into the formula:
\( P = 2\times[(5.5y + 7) + (7y - 5.5)] \)

Step3: Simplify Inside the Brackets

Combine like terms: \( 5.5y + 7y = 12.5y \) and \( 7 - 5.5 = 1.5 \). So inside the brackets we have \( 12.5y + 1.5 \).

Step4: Multiply by 2

\( P = 2\times(12.5y + 1.5) = 2\times12.5y + 2\times1.5 = 25y + 3 \)

Answer:

\( 25y + 3 \)