Question

corey is doing renovations to his living room.
the length of the room is 25 feet and the width is 12 feet.
a scale drawing of the room has a width of 24 inches.
what is the perimeter of the scale drawing?
inches
calculator
(image: two rectangles, larger one labeled 25 ft (length) and 12 ft (width), smaller one labeled 24 in (width); note: image is not drawn to scale)

Explanation:

Step1: Find the scale factor

The actual width is 12 feet, and the scale - drawing width is 24 inches. First, convert 12 feet to inches. Since 1 foot = 12 inches, 12 feet = \(12\times12 = 144\) inches. The scale factor \(k=\frac{\text{scale - drawing width}}{\text{actual width}}=\frac{24}{144}=\frac{1}{6}\).

Step2: Find the length of the scale - drawing

The actual length is 25 feet. Convert 25 feet to inches: \(25\times12 = 300\) inches. The length of the scale - drawing \(l = 300\times\frac{1}{6}=50\) inches.

Step3: Calculate the perimeter of the scale - drawing

The scale - drawing is a rectangle with length \(l = 50\) inches and width \(w = 24\) inches. The formula for the perimeter of a rectangle is \(P = 2(l + w)\). Substitute \(l = 50\) and \(w = 24\) into the formula: \(P=2(50 + 24)=2\times74 = 148\) inches.

Answer:

148