Question

question 1 of 5
a gardener made a scale drawing of a lawn with a scale factor of 1:15. the dimensions of his drawing are 6 inches long by 3 inches wide. his partner plans to make another scale drawing of the lawn, but with a scale factor of 1:5.
what are the dimensions of his scale drawing?
a. the length is 18 inches and the width is 9 inches.
b. the length is 9 inches and the width is 18 inches.
c. the length is 1 inch and the width is 2 inches.
d. the length is 2 inches and the width is 1 inch.

Explanation:

Step1: Find the actual length and width of the lawn

Since the scale factor of the first drawing is \(1:15\), and the drawing length is \(6\) inches and width is \(3\) inches.
Let the actual length be \(L\) and actual width be \(W\).
For length: \(\frac{6}{L}=\frac{1}{15}\), so \(L = 6\times15=90\) inches.
For width: \(\frac{3}{W}=\frac{1}{15}\), so \(W = 3\times15 = 45\) inches.

Step2: Find the dimensions of the second - scale drawing

The scale factor of the second drawing is \(1:5\).
Let the length of the second drawing be \(l\) and width be \(w\).
For length: \(\frac{l}{90}=\frac{1}{5}\), then \(l=\frac{90}{5}=18\) inches.
For width: \(\frac{w}{45}=\frac{1}{5}\), then \(w=\frac{45}{5}=9\) inches.

Answer:

A. The length is 18 inches and the width is 9 inches.