Question

5.6 ps - 15
the width of a rectangle is ( 7n - 4.5 ) feet and the length is ( 4.5n + 9 ) 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 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

Given \(w=7n - 4.5\) and \(l = 4.5n+9\). Then \(P=2[(4.5n + 9)+(7n - 4.5)]\).
First, simplify the expression inside the brackets: \((4.5n+9)+(7n - 4.5)=4.5n+7n+9 - 4.5=(4.5 + 7)n+(9 - 4.5)=11.5n + 4.5\).

Step3: Multiply by 2

\(P=2(11.5n + 4.5)\). Using the distributive property \(a(b + c)=ab+ac\), we get \(P=2\times11.5n+2\times4.5\).
Since \(2\times11.5n = 23n\) and \(2\times4.5 = 9\).

Answer:

\(23n + 9\)