Question

the perimeter of a rectangular painting is 342 centimeters. if the width of the painting is 78 centimeters, what is its length?
centimeters

Explanation:

Step1: Recall the perimeter formula of a rectangle

The perimeter \( P \) of a rectangle is given by the formula \( P = 2\times (l + w) \), where \( l \) is the length and \( w \) is the width. We know \( P = 342 \) cm and \( w = 78 \) 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: \( \frac{342}{2}=l + 78 \).
Calculating \( \frac{342}{2} \), we get \( 171=l + 78 \).

Step2: Solve for the length \( l \)

To find \( l \), we subtract the width \( w \) from both sides of the equation \( 171=l + 78 \). So, \( l=171 - 78 \).
Calculating \( 171-78 \), we get \( l = 93 \).

Answer:

The length of the rectangular painting is 93 centimeters.