Question

1. josie is drawing a horse to scale. if the horse is 5 feet tall and 8 feet long, what are the dimensions (in inches) of a 1:20 scale drawing? will it fit on an 8.5 - inch × 11 - inch sheet of paper?

Explanation:

Step1: Convert feet to inches

Since \(1\) foot \( = 12\) inches, the actual height \(h_{actual}=5\times12 = 60\) inches and the actual length \(l_{actual}=8\times12=96\) inches.

Step2: Use the scale formula

The scale formula is \(\text{Scale}=\frac{\text{Model dimension}}{\text{Actual dimension}}\). Let the model height be \(h_{model}\) and model length be \(l_{model}\). Given scale \(s = \frac{1}{20}\).
For height: \(\frac{1}{20}=\frac{h_{model}}{60}\), then \(h_{model}=\frac{60}{20}=3\) inches.
For length: \(\frac{1}{20}=\frac{l_{model}}{96}\), then \(l_{model}=\frac{96}{20}=4.8\) inches.

Step3: Compare with paper size

The paper size is \(8.5\times11\) inches. The model dimensions are \(3\) inches (height) and \(4.8\) inches (length). Since \(3<8.5\) and \(4.8 < 11\).

Answer:

The dimensions of the scale - drawing are \(3\) inches (height) and \(4.8\) inches (length). Yes, it will fit on an \(8.5 - \text{inch}\times11-\text{inch}\) sheet of paper.