Question

nora is doing renovations to her living room.
the length of the room is 24 feet and the width is 13 feet.
a scale drawing of the room has a width of 26 inches.
what is the perimeter of the scale drawing?
inches
calculator
13 ft.
24 ft.
26 in.
image is not drawn to scale.

Explanation:

Step1: Find the scale factor

The actual width is 13 feet, and the scale - drawing width is 26 inches. First, we need to find the scale factor. Since 13 feet corresponds to 26 inches, the scale factor (in terms of inches per foot) is $\frac{26\ inches}{13\ feet}=2\ inches\ per\ foot$.

Step2: Find the length of the scale - drawing

The actual length of the room is 24 feet. Using the scale factor of 2 inches per foot, the length of the scale - drawing is $24\ feet\times2\ inches\ per\ foot = 48\ inches$.

Step3: Calculate the perimeter of the scale - drawing

The scale - drawing is a rectangle with length $l = 48$ inches and width $w = 26$ inches. The formula for the perimeter of a rectangle is $P=2(l + w)$.
Substitute $l = 48$ and $w = 26$ into the formula: $P = 2(48+26)$.
First, calculate the sum inside the parentheses: $48 + 26=74$.
Then, multiply by 2: $2\times74 = 148$.

Answer:

148