Question

Find equivalent ratios of the corresponding side lengths from the scale drawings to the garden.

Scale drawing
6 in
8 in
10 in

Community garden
24 ft
32 ft
40 ft

Ratio
A 4 in.:1 ft
B 1 in. : 4 ft
C 4 in. : 1 ft
D 6 in. : 1 ft





Scale drawing: 53, 37
Actual community garden: 53 37

Answer 1

To find equivalent ratios of the corresponding side lengths from the scale drawings to the actual garden, we can start by converting both measurements to the same unit.

1. **Convert the scale drawing to feet**:
- The lengths in the scale drawing are given in inches, so we need to convert them to feet.
- There are 12 inches in a foot.

Therefore, we convert the lengths:
- \( 6 \text{ in} = \frac{6}{12} = 0.5 \text{ ft} \)
- \( 8 \text{ in} = \frac{8}{12} = \frac{2}{3} \text{ ft} \)
- \( 10 \text{ in} = \frac{10}{12} = \frac{5}{6} \text{ ft} \)

2. **Corresponding side lengths of the community garden**:
- 24 ft
- 32 ft
- 40 ft

3. **Create the ratios**:
- The ratios of the scale drawing to the actual garden are:
- For 6 in. (0.5 ft) to 24 ft:
\[
\frac{0.5 \text{ ft}}{24 \text{ ft}} = \frac{1}{48}
\]
- For 8 in. (\(\frac{2}{3}\) ft) to 32 ft:
\[
\frac{\frac{2}{3} \text{ ft}}{32 \text{ ft}} = \frac{2}{96} = \frac{1}{48}
\]
- For 10 in. (\(\frac{5}{6}\) ft) to 40 ft:
\[
\frac{\frac{5}{6} \text{ ft}}{40 \text{ ft}} = \frac{5}{240} = \frac{1}{48}
\]

4. **Identify the equivalent ratios**:
- Each of the ratios above simplifies down to the same value, which gives us an overall ratio of 1:48.

Now let’s match the ratios given in the answer choices:
- **A: 4 in. : 1 ft** → This converts to \( \frac{4}{12} : 1 = \frac{1}{3} \), not equivalent.
- **B: 1 in. : 4 ft** → This converts to \( \frac{1}{12} : 1 \), not equivalent.
- **C: 4 in. : 1 ft** → Identical to A, also not equivalent.
- **D: 6 in. : 1 ft** → This converts to \( \frac{6}{12} : 1 = \frac{1}{2} \), not equivalent.

None of the provided ratios are equivalent to \( \frac{1}{48} \).

However, if there are other specific numbers or contexts that need to be addressed for the modified side lengths (53, 37) in either the scale drawing or the garden, feel free to provide additional details for further assistance!