Question

a rectangle has a perimeter of 12 inches. if the width of the rectangle is $4\frac{4}{5}$ inches, what is the length of the rectangle? explain how you know.

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by the formula \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width. We know \( P = 12 \) inches and \( w = 4\frac{4}{5} \) inches. First, we can simplify the formula to solve for \( l \). Divide both sides of the formula by 2: \( \frac{P}{2}=l + w \). Then, rearrange to solve for \( l \): \( l=\frac{P}{2}-w \).

Step2: Convert the mixed number to an improper fraction and calculate \( \frac{P}{2} \)

First, convert \( 4\frac{4}{5} \) to an improper fraction. \( 4\frac{4}{5}=\frac{4\times5 + 4}{5}=\frac{24}{5} \). Then, calculate \( \frac{P}{2} \). Since \( P = 12 \), \( \frac{12}{2}=6 \).

Step3: Subtract the width from \( \frac{P}{2} \) to find the length

Now, we need to find \( l = 6-\frac{24}{5} \). Convert 6 to a fraction with a denominator of 5: \( 6=\frac{30}{5} \). Then, subtract: \( \frac{30}{5}-\frac{24}{5}=\frac{30 - 24}{5}=\frac{6}{5} \). Convert \( \frac{6}{5} \) back to a mixed number: \( \frac{6}{5}=1\frac{1}{5} \).

Answer:

The length of the rectangle is \( 1\frac{1}{5} \) inches.