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The greatest possible length which can be used to measure exactly the lengths 1m 92cm,3m 84cm ,23m 4cm
- a)23
- b)32
- c)36
- d)34
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The greatest possible length which can be used to measure exactly the ...
192 = 42×22×3
384 = 42×22×6
2304 = 42×2×62
HCF = 42×2 = 16×2 = 32
384 = 42×22×6
2304 = 42×2×62
HCF = 42×2 = 16×2 = 32
Most Upvoted Answer
The greatest possible length which can be used to measure exactly the ...
192 = 42×22×3
384 = 42×22×6
2304 = 42×2×62
HCF = 42×2 = 16×2 = 32
384 = 42×22×6
2304 = 42×2×62
HCF = 42×2 = 16×2 = 32
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Community Answer
The greatest possible length which can be used to measure exactly the ...
Problem:
The question asks for the greatest possible length that can be used to measure exactly the lengths 1m 92cm, 3m 84cm, and 23m 4cm.
Approach:
To find the greatest possible length that can be used to measure these lengths exactly, we need to find the greatest common divisor (GCD) of the given lengths. The GCD will give us the length that can evenly divide all the given lengths.
Solution:
To find the GCD, we can use the Euclidean algorithm. Here are the steps to find the GCD:
1. Convert all the lengths to the same unit. In this case, let's convert them to centimeters.
- 1m 92cm = 100cm + 92cm = 192cm
- 3m 84cm = 300cm + 84cm = 384cm
- 23m 4cm = 2300cm + 4cm = 2304cm
2. Find the GCD of the two smallest lengths first. In this case, the two smallest lengths are 192cm and 384cm.
- Divide 384cm by 192cm: 384 ÷ 192 = 2
- The remainder is 0, so the GCD is 192cm.
3. Find the GCD of the result from step 2 and the next length. In this case, the result from step 2 is 192cm and the next length is 2304cm.
- Divide 2304cm by 192cm: 2304 ÷ 192 = 12
- The remainder is 0, so the GCD is 192cm.
Answer:
Therefore, the greatest possible length that can be used to measure exactly the lengths 1m 92cm, 3m 84cm, and 23m 4cm is 192cm. The correct answer is option 'B'.
The question asks for the greatest possible length that can be used to measure exactly the lengths 1m 92cm, 3m 84cm, and 23m 4cm.
Approach:
To find the greatest possible length that can be used to measure these lengths exactly, we need to find the greatest common divisor (GCD) of the given lengths. The GCD will give us the length that can evenly divide all the given lengths.
Solution:
To find the GCD, we can use the Euclidean algorithm. Here are the steps to find the GCD:
1. Convert all the lengths to the same unit. In this case, let's convert them to centimeters.
- 1m 92cm = 100cm + 92cm = 192cm
- 3m 84cm = 300cm + 84cm = 384cm
- 23m 4cm = 2300cm + 4cm = 2304cm
2. Find the GCD of the two smallest lengths first. In this case, the two smallest lengths are 192cm and 384cm.
- Divide 384cm by 192cm: 384 ÷ 192 = 2
- The remainder is 0, so the GCD is 192cm.
3. Find the GCD of the result from step 2 and the next length. In this case, the result from step 2 is 192cm and the next length is 2304cm.
- Divide 2304cm by 192cm: 2304 ÷ 192 = 12
- The remainder is 0, so the GCD is 192cm.
Answer:
Therefore, the greatest possible length that can be used to measure exactly the lengths 1m 92cm, 3m 84cm, and 23m 4cm is 192cm. The correct answer is option 'B'.
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