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 1 in. to 4 ft 8 in. 32 ft? 10 in. 40 ft

Explanation:

Step1: Identify given scale ratio

We know from the first row: 6 in. (scale) corresponds to 24 ft (actual). The ratio is $\frac{1\text{ in.}}{4\text{ ft}}$.

Step2: Verify/derive ratio for 8 in.

Set up proportion: $\frac{\text{Scale length}}{\text{Actual length}} = \frac{1}{4}$
Substitute scale length = 8 in.:
$\frac{8}{\text{Actual length}} = \frac{1}{4}$
Solve for actual length: $\text{Actual length} = 8 \times 4 = 32$ ft, so the ratio for this row is $\frac{8\text{ in.}}{32\text{ ft}} = \frac{1\text{ in.}}{4\text{ ft}}$

Step3: Simplify to equivalent ratio

Simplify the ratio by dividing numerator and denominator by their greatest common divisor (for 8 and 32, GCD is 8):
$\frac{8\div8}{32\div8} = \frac{1\text{ in.}}{4\text{ ft}}$

Answer:

The equivalent ratio for the 8 in. scale length is $\frac{1\text{ in.}}{4\text{ ft}}$ (or simplified as 1 in. to 4 ft, matching the first row's ratio).