Question

Imogen sees a design for a garden in a magazine. She changes the scale because she wants a smaller garden. The figure below shows both scales and a scale drawing of the yard

Magazine scale: 1 inch = 3.5 feet. Imogen's scale: 2 inches = 6 feet. Triangle A B C. Side A is 8 inches, side B is 5 inches, and side C is 10 inches.

Which statements about the gardens are true? Select three options.
Length A of the magazine’s garden is 28 ft.
Length A of Imogen’s garden is 28 ft.
Length B of the magazine’s garden is 17.5 ft.
Length B of Imogen’s garden is 18 ft.
Length C of the magazine’s garden is 35 ft.
Length C of Imogen’s garden is 20 ft.

Answer 1

To determine the true statements about the gardens, we need to convert the measurements of each side length from inches to feet according to the given scales.

1. **Magazine Scale: 1 inch = 3.5 feet**
- Length A (8 inches):
\( 8 \text{ inches} \times 3.5 \text{ feet/inch} = 28 \text{ feet} \)
- Length B (5 inches):
\( 5 \text{ inches} \times 3.5 \text{ feet/inch} = 17.5 \text{ feet} \)
- Length C (10 inches):
\( 10 \text{ inches} \times 3.5 \text{ feet/inch} = 35 \text{ feet} \)

2. **Imogen's Scale: 2 inches = 6 feet**
- To convert inches to feet, we can use the conversion of 2 inches to 6 feet. This means that 1 inch = 3 feet.
- Length A (8 inches):
\( 8 \text{ inches} \times 3 \text{ feet/inch} = 24 \text{ feet} \)
- Length B (5 inches):
\( 5 \text{ inches} \times 3 \text{ feet/inch} = 15 \text{ feet} \)
- Length C (10 inches):
\( 10 \text{ inches} \times 3 \text{ feet/inch} = 30 \text{ feet} \)

Now, let's examine the given statements:

1. **Length A of the magazine's garden is 28 ft.**
- True (Calculated earlier)

2. **Length A of Imogen’s garden is 28 ft.**
- False (It's actually 24 ft)

3. **Length B of the magazine’s garden is 17.5 ft.**
- True (Calculated earlier)

4. **Length B of Imogen’s garden is 18 ft.**
- False (It's actually 15 ft)

5. **Length C of the magazine’s garden is 35 ft.**
- True (Calculated earlier)

6. **Length C of Imogen’s garden is 20 ft.**
- False (It's actually 30 ft)

Therefore, the true statements are:

- Length A of the magazine's garden is 28 ft.
- Length B of the magazine's garden is 17.5 ft.
- Length C of the magazine's garden is 35 ft.