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
?

6 in.
scale drawing
8 in.
10 in.

Explanation:

Step1: Find ratio for first pair

To find the ratio of scale - drawing length to actual length, use the first pair of values. For a scale - drawing length of 6 in and an actual length of 24 ft. First, make the units the same. Since 1 ft = 12 in, 24 ft=24×12 = 288 in. The ratio is $\frac{6}{288}=\frac{1}{48}$.

Step2: Check other pairs

For the second pair, scale - drawing length is 8 in. Let the actual length be $x$ inches. Since the ratio is $\frac{1}{48}$, we have $\frac{8}{x}=\frac{1}{48}$, so $x = 8\times48=384$ in. And 384 in = 32 ft. For the third pair, scale - drawing length is 10 in. Let the actual length be $y$ inches. Using the ratio $\frac{1}{48}$, we have $\frac{10}{y}=\frac{1}{48}$, so $y = 10\times48 = 480$ in. And 480 in = 40 ft.

Answer:

$\frac{1}{48}$