Question

question the length and width of a rectangle are consecutive odd integers. the perimeter of the rectangle is 96 centimeters. find the length and width of the rectangle. answer width = centimeters length = centimeters

Explanation:

Step1: Let the width be \(x\)

Since length and width are consecutive odd integers, length \(=x + 2\)
Perimeter of rectangle \(P=2\times(\text{length}+\text{width})\)
Given \(P = 96\)
So \(2\times(x+(x + 2))=96\)

Step2: Simplify the equation

\(2\times(2x+2)=96\)
\(4x + 4=96\)
\(4x=96 - 4\)
\(4x=92\)
\(x = 23\)

Step3: Find the length

Length \(=x + 2=23+2 = 25\)

Answer:

Width \(=23\) centimeters, Length \(=25\) centimeters