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
A 4 in.:1 ft
B 1 in. : 4 ft
C 4 in. : 1 ft
D 6 in. : 1 ft
Scale drawing: 53, 37
Actual community garden: 53 37
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
A 4 in.:1 ft
B 1 in. : 4 ft
C 4 in. : 1 ft
D 6 in. : 1 ft
Scale drawing: 53, 37
Actual community garden: 53 37
Answers
Answered by
GPT-4o mini
To find equivalent ratios of the corresponding side lengths from the scale drawings to the actual community garden, we can use the given measurements and check them against the provided ratios.
Given the scale drawing with lengths in inches and the actual garden dimensions in feet, we convert everything to the same unit to easily find the ratios. Let's analyze the first pair of dimensions.
1. **For the first ratio: 6 in. to 24 ft**
- We can convert 24 ft to inches (since 1 ft = 12 inches):
- \( 24 \, \text{ft} = 24 \times 12 = 288 \, \text{in.} \)
- The ratio then becomes \( 6 \, \text{in.} : 288 \, \text{in.} \).
- To simplify the ratio, divide both sides by 6:
- \( 1 : 48 \).
2. **For the second ratio: 8 in. to 32 ft**
- Convert 32 ft to inches:
- \( 32 \, \text{ft} = 32 \times 12 = 384 \, \text{in.} \)
- The ratio is \( 8 \, \text{in.} : 384 \, \text{in.} \).
- Simplify by dividing by 8:
- \( 1 : 48 \).
3. **For the third ratio: 10 in. to 40 ft**
- Convert 40 ft to inches:
- \( 40 \, \text{ft} = 40 \times 12 = 480 \, \text{in.} \)
- The ratio becomes \( 10 \, \text{in.} : 480 \, \text{in.} \).
- Simplify by dividing by 10:
- \( 1 : 48 \).
Now, we compare these results to the given ratios:
- From the calculation, we have the same ratio of **1 : 48** for all three pairs of dimensions.
For the provided options (A, B, C, D):
- Option A (4 in : 1 ft) converts to 48 : 12, simplified to 4:1,
- Option B (1 in : 4 ft) gives us a ratio of 1:48,
- Option C (4 in : 1 ft) same as A, 4:1,
- Option D (6 in : 1 ft), which is not a match since the actual ratio was 1:48.
Thus, the equivalent ratio for the given lengths in the scale drawing to the garden is **B (1 in. : 4 ft)**.
Given the scale drawing with lengths in inches and the actual garden dimensions in feet, we convert everything to the same unit to easily find the ratios. Let's analyze the first pair of dimensions.
1. **For the first ratio: 6 in. to 24 ft**
- We can convert 24 ft to inches (since 1 ft = 12 inches):
- \( 24 \, \text{ft} = 24 \times 12 = 288 \, \text{in.} \)
- The ratio then becomes \( 6 \, \text{in.} : 288 \, \text{in.} \).
- To simplify the ratio, divide both sides by 6:
- \( 1 : 48 \).
2. **For the second ratio: 8 in. to 32 ft**
- Convert 32 ft to inches:
- \( 32 \, \text{ft} = 32 \times 12 = 384 \, \text{in.} \)
- The ratio is \( 8 \, \text{in.} : 384 \, \text{in.} \).
- Simplify by dividing by 8:
- \( 1 : 48 \).
3. **For the third ratio: 10 in. to 40 ft**
- Convert 40 ft to inches:
- \( 40 \, \text{ft} = 40 \times 12 = 480 \, \text{in.} \)
- The ratio becomes \( 10 \, \text{in.} : 480 \, \text{in.} \).
- Simplify by dividing by 10:
- \( 1 : 48 \).
Now, we compare these results to the given ratios:
- From the calculation, we have the same ratio of **1 : 48** for all three pairs of dimensions.
For the provided options (A, B, C, D):
- Option A (4 in : 1 ft) converts to 48 : 12, simplified to 4:1,
- Option B (1 in : 4 ft) gives us a ratio of 1:48,
- Option C (4 in : 1 ft) same as A, 4:1,
- Option D (6 in : 1 ft), which is not a match since the actual ratio was 1:48.
Thus, the equivalent ratio for the given lengths in the scale drawing to the garden is **B (1 in. : 4 ft)**.
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