Question

use the situation below to answer questions 1 & 2.
the perimeter of a rectangle is 54 inches. its length is 15 inches.

1. which equation will calculate the width (w) of the rectangle? *

p = 54 + 15
2w + 15 = 54
2(w + 15) = 54
w + 15 = 54

1. what is the width (w) of the rectangle described above? *

the rectangle has a width of 19.5 inches.
the rectangle has a width of 12 inches.
the rectangle has a width of 27 inches.
the rectangle has a width of 7.5 inches.

Explanation:

Step1: Recall the perimeter formula

The perimeter formula of a rectangle is \(P = 2(l + w)\), where \(P\) is the perimeter, \(l\) is the length, and \(w\) is the width. Given \(P = 54\) inches and \(l=15\) inches. Substitute into the formula: \(2(w + 15)=54\).

Step2: Solve the equation for \(w\)

Divide both sides of the equation \(2(w + 15)=54\) by 2:

$$\begin{align*} \frac{2(w + 15)}{2}&=\frac{54}{2}\\ w + 15&=27 \end{align*}$$

Subtract 15 from both sides: \(w=27 - 15=12\)

Answer:

1. \(2(w + 15)=54\)
2. The rectangle has a width of 12 inches.