Question

the actual lengths of the garden are shown in the table. choose an equivalent ratio that shows each length in the scale drawing to the length in the garden.
length in scale drawing | actual length in garden | ratio
6 in. | 24 ft | ?
8 in. | 32 ft |
10 in. | 40 ft |
(there is also a triangle labeled scale drawing with sides 6 in., 8 in., 10 in. below the table)

Explanation:

Step1: Convert units to same type

First, convert feet to inches (1 ft = 12 in):
$24\ \text{ft} = 24 \times 12 = 288\ \text{in}$

Step2: Simplify the scale ratio

Use the first pair of values to find the ratio of scale drawing length to actual length:
$\text{Ratio} = \frac{6\ \text{in}}{288\ \text{in}} = \frac{1}{48}$

Step3: Verify with other pairs

Check the second pair: $\frac{8\ \text{in}}{32 \times 12\ \text{in}} = \frac{8}{384} = \frac{1}{48}$
Check the third pair: $\frac{10\ \text{in}}{40 \times 12\ \text{in}} = \frac{10}{480} = \frac{1}{48}$

Answer:

The equivalent ratio of scale drawing length to actual garden length is $\frac{1}{48}$ (or 1 in : 48 in, which simplifies to 1 in : 4 ft)