Question

in a scale model of a boat, 1 inch represents 9 feet.
scale
1 in : 9 ft
answer the following.
(a) the height of the real boat is 63 feet. what is the height of the boat in the scale model?
□ inches
(b) in the scale model, the length of the boat is 10 inches. what is the length of the real boat?
□ feet

Explanation:

Part (a)

Step1: Understand the scale

The scale is \( 1 \) inch represents \( 9 \) feet, so the ratio of model inches to real feet is \( \frac{1 \text{ inch}}{9 \text{ feet}} \).

Step2: Set up the proportion

Let \( x \) be the height of the model in inches. We know the real height is \( 63 \) feet. So we set up the proportion:

$$ \frac{x \text{ inches}}{63 \text{ feet}} = \frac{1 \text{ inch}}{9 \text{ feet}} $$

Step3: Solve for \( x \)

Cross - multiply: \( 9x=63\times1 \)
Then, \( x = \frac{63}{9} \)
\( x = 7 \)

Part (b)

Step1: Use the scale ratio

The scale is \( 1 \) inch (model) : \( 9 \) feet (real). If the model length is \( 10 \) inches.

Step2: Calculate the real length

To find the real length, we multiply the model length by the scale factor (since \( 1 \) inch model = \( 9 \) feet real). So the real length \( L=10\times9 \)
\( L = 90 \)

Answer:

s:
(a) \( 7 \) inches
(b) \( 90 \) feet