Question

use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object. scale factor: 3:1 6 in 15 in scale drawing object a. side a is 12 inches long and side b is 4 inches long. b. side a is 45 inches long and side b is 18 inches long. c. side a is 5 inches long and side b is 2 inches long. d. side a is 12 inches long and side b is 3 inches long.

Explanation:

Step1: Recall the scale - factor formula

The scale factor formula is \(\text{Scale Factor}=\frac{\text{Scale Drawing Length}}{\text{Real Object Length}}\). Given the scale factor \(3:1=\frac{3}{1}\), if \(x\) is the length of the scale - drawing and \(y\) is the length of the real object, then \(\frac{x}{y}=\frac{3}{1}\), or \(y = \frac{x}{3}\).

Step2: Calculate the length of side \(a\)

For the side of length \(15\) inches in the scale - drawing. Using the formula \(y=\frac{x}{3}\), when \(x = 15\) inches (scale - drawing length), then \(a=\frac{15}{3}=5\) inches.

Step3: Calculate the length of side \(b\)

For the side of length \(6\) inches in the scale - drawing. Using the formula \(y=\frac{x}{3}\), when \(x = 6\) inches (scale - drawing length), then \(b=\frac{6}{3}=2\) inches.

Answer:

C. Side \(a\) is \(5\) inches long and side \(b\) is \(2\) inches long.