Question

the length and width of a rectangle are consecutive odd integers. the perimeter of the rectangle is 104 centimeters. find the length and width of the rectangle.
answer
width = \square centimeters \quad length = \square centimeters \quad submit answer

Explanation:

Step1: Define variables

Let the width be \( x \) (an odd integer), then the length, being the next consecutive odd integer, is \( x + 2 \).

Step2: Use the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2(\text{length} + \text{width}) \). We know \( P = 104 \), so we substitute the expressions for length and width into the formula:
\[
104 = 2((x + 2) + x)
\]

Step3: Simplify and solve for \( x \)

First, simplify the right - hand side:
\[
104 = 2(2x + 2)
\]
Divide both sides by 2:
\[
52=2x + 2
\]
Subtract 2 from both sides:
\[
50 = 2x
\]
Divide both sides by 2:
\[
x = 25
\]

Step4: Find the length

Since the length is \( x + 2 \), substitute \( x = 25 \):
\[
\text{Length}=25 + 2=27
\]

Answer:

Width = \( 25 \) centimeters, Length = \( 27 \) centimeters