Question

the perimeter of a rectangular door is 460 centimeters. the width is 133 centimeters. what is the length, in centimeters, of the door?

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 \( P = 460 \) cm and \( w = 133 \) cm, and we need to find \( l \). First, we can divide both sides of the formula by 2 to simplify: \( \frac{P}{2}=l + w \).
Substituting the known values, we get \( \frac{460}{2}=l + 133 \).

Step2: Simplify the left - hand side

Calculate \( \frac{460}{2} \), which equals 230. So the equation becomes \( 230=l + 133 \).

Step3: Solve for \( l \)

To find \( l \), we subtract 133 from both sides of the equation: \( l=230 - 133 \).
Calculating \( 230-133 \), we get \( l = 97 \).

Answer:

The length of the door is 97 centimeters.