Question

the width of a rectangle is 6x - 7.5 feet and the length is 7.5x + 8 feet. find the perimeter of the rectangle. the perimeter of the rectangle is \boxed{} feet. (simplify your answer. use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Let \( l = 7.5x + 8 \) (length) and \( w = 6x - 7.5 \) (width).

Step2: Substitute length and width into the formula

First, find \( l + w \):
\( (7.5x + 8)+(6x - 7.5)=7.5x + 6x+8 - 7.5 = 13.5x + 0.5 \)
Then, multiply by 2 to get the perimeter:
\( P = 2\times(13.5x + 0.5)=2\times13.5x+2\times0.5 = 27x + 1 \)

Answer:

The perimeter of the rectangle is \( 27x + 1 \) feet.