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.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
18 days ago

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.