Question

A house that is 44 feet tall by 64 feet wide is to be modeled in miniature by a figure that is 10 inches wide. What is the height of the model house?
13.91 inches
9.16 inches
6.88 inches
14.55 inches

Answer 1

To find the height of the model house, we can use the scale ratio based on the width of the actual house and the width of the model.

1. **Convert the dimensions of the house to the same units**:
- The actual house is 64 feet wide.
- The width of the model house is 10 inches.

First, convert the width of the actual house from feet to inches:
\[
64 \text{ feet} \times 12 \text{ inches/foot} = 768 \text{ inches}
\]

2. **Determine the scale ratio**:
The scale ratio is the width of the model divided by the width of the actual house:
\[
\text{Scale ratio} = \frac{\text{Width of model}}{\text{Width of actual house}} = \frac{10 \text{ inches}}{768 \text{ inches}}
\]

3. **Calculate the height of the model house using the scale ratio**:
Now, we can find the height of the model based on the actual height of the house, which is 44 feet. Convert the height to inches:
\[
44 \text{ feet} \times 12 \text{ inches/foot} = 528 \text{ inches}
\]

Now, multiply the actual height by the scale ratio:
\[
\text{Height of model} = \text{Actual height} \times \text{Scale ratio} = 528 \text{ inches} \times \frac{10}{768}
\]

4. **Calculate the height**:
\[
\text{Height of model} = 528 \times \frac{10}{768} \approx 6.88 \text{ inches}
\]

So, the height of the model house is approximately \( **6.88 \text{ inches}** \).

Thus, the correct answer is:
**6.88 inches**.