Question

question 1 of 15
steffie makes a scale drawing for a crate with a scale factor of 1:3. the dimensions of her scale drawing are 15 inches long by 12 inches wide. the builder creates a scale drawing of the crate with a scale factor of 1:9.
what are the dimensions of the builders scale drawing?
a. the length is 4 inches and the width is 5 inches.
b. the length is 45 inches and the width is 36 inches.
c. the length is 5 inches and the width is 4 inches.
d. the length is 36 inches and the width is 45 inches.

Explanation:

Step1: Find the actual length of the crate

Given Steffie's scale factor \(1:3\) and her drawing length \(15\) inches. Let the actual length be \(x\). Using the scale ratio \(\frac{1}{3}=\frac{15}{x}\), then \(x = 15\times3=45\) inches.

Step2: Find the builder's drawing length

The builder's scale factor is \(1:9\). Let the builder's drawing length be \(y\). Using the scale ratio \(\frac{1}{9}=\frac{y}{45}\), then \(y=\frac{45}{9} = 5\) inches.

Step3: Find the actual width of the crate

Given Steffie's scale factor \(1:3\) and her drawing width \(12\) inches. Let the actual width be \(m\). Using the scale ratio \(\frac{1}{3}=\frac{12}{m}\), then \(m = 12\times3=36\) inches.

Step4: Find the builder's drawing width

The builder's scale factor is \(1:9\). Let the builder's drawing width be \(n\). Using the scale ratio \(\frac{1}{9}=\frac{n}{36}\), then \(n=\frac{36}{9}=4\) inches.

Answer:

C. The length is 5 inches and the width is 4 inches.