Question

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

Scale drawing Community garden. Ratios
6 in. 24 ft. Ratio
A 4 in.:1 ft
B 1 in. : 4 ft
C 4 in. : 1 ft
D 6 in. : 1 ft
8 in. 32 ft
10 in. 40 ft

Ratio
1 in. : 4 ft

A 1 in. : 4 ft
C 4 in. : 1 ft
D 8 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 sizes, we can establish the ratios based on the scale given.

From the first example, we notice that:
- The scale drawing is 6 inches and the actual garden size is 24 feet.
- To establish the corresponding ratio:
\[
\text{Ratio} = \frac{6 \text{ in.}}{24 \text{ ft.}} = \frac{1}{4}
\]
- This is equivalent to 1 inch : 4 feet.

Next, we check the ratios given in the options:
- **A: 4 in. : 1 ft** is not equivalent to the 1 in. : 4 ft.
- **B: 1 in. : 4 ft** is equivalent.
- **C: 4 in. : 1 ft** is not equivalent.
- **D: 6 in. : 1 ft** is not equivalent.

Therefore, the correct answer from the first set is:
- **B: 1 in. : 4 ft**

For the second set of ratios, involving 8 in. and 32 ft:
- The ratio can also be calculated similarly:
\[
\text{Ratio} = \frac{8 \text{ in.}}{32 \text{ ft.}} = \frac{1}{4}
\]
This simplifies to 1 inch : 4 feet.

We note that the options provided match:
- **A: 1 in. : 4 ft** is equivalent.
- **C: 4 in. : 1 ft** is not equivalent.
- **D: 8 in. : 1 ft** is not equivalent.

Thus, for the second example, the answer is also:
- **A: 1 in. : 4 ft**

In conclusion, the equivalent ratio for both cases is:
- **1 in. : 4 ft**.