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. table with rows: 6 in. (scale) - 24 ft (actual) -?; 8 in. - 32 ft - ; 10 in. - 40 ft - triangle scale drawing: 6 in., 8 in., 10 in.

Explanation:

Step1: Convert units (optional, but for ratio, we can use inches to feet or simplify the ratio of inches to feet directly. Let's take the first row: length in scale drawing is 6 in, actual is 24 ft. First, make sure units are consistent? Wait, the ratio is scale drawing length to garden length, so we can write the ratio as 6 in : 24 ft. But we can simplify this ratio. Let's convert 24 ft to inches? Wait, 24 ft = 24 12 = 288 in. Then the ratio is 6 in : 288 in = 6/288 = 1/48? Wait, no, that seems off. Wait, maybe the ratio is in inches to feet, but we can simplify the numbers. Wait, 6 in and 24 ft. Let's divide both by 6: 6/6 = 1, 24/6 = 4. Wait, no, 6 in : 24 ft. Wait, maybe the ratio is 6 in : 24 ft = 1 in : 4 ft (dividing both by 6). Let's check the second row: 8 in : 32 ft. 8/8 = 1, 32/8 = 4. So 1 in : 4 ft. Third row: 10 in : 40 ft. 10/10 = 1, 40/10 = 4. So the ratio is 1 in : 4 ft, or 6 in : 24 ft simplifies to 1:4 (when considering inches to feet? Wait, no, the units are different, but the ratio can be written as 6 in / 24 ft = (6/24) in/ft = 1/4 in/ft. Wait, maybe the ratio is 6 in : 24 ft = 1 in : 4 ft (since 6/24 = 1/4, so 1 in of scale drawing corresponds to 4 ft of actual length). Let's verify: 1 in 4 ft/in = 4 ft? Wait, no, 6 in scale is 24 ft actual, so 24 ft / 6 in = 4 ft per inch. So the ratio of scale length (in inches) to actual length (in feet) is 6:24 = 1:4, 8:32 = 1:4, 10:40 = 1:4. So the equivalent ratio for the first row is 6 in : 24 ft = 1 in : 4 ft (or 6:24 simplifies to 1:4).

Step2: Simplify the ratio 6 in : 24 ft. Divide both parts by 6: 6 ÷ 6 = 1, 24 ÷ 6 = 4. So the ratio is 1 in : 4 ft (or 6:24 = 1:4).

Answer:

The equivalent ratio is \( 1 \text{ in} : 4 \text{ ft} \) (or \( 6:24 = 1:4 \) when simplified).