Question:
Two vertical poles of height 6 m and 18 m are 10 m apart on a flat ground. A string needs to be connected from the top of one pole to a peg on the ground and then on to the top of the other pole. The minimum length (m) of the string is
Two vertical poles of height 6 m and 18 m are 10 m apart on a flat ground. A string needs to be connected from the top of one pole to a peg on the ground and then on to the top of the other pole. The minimum length (m) of the string is
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- The Pythagorean theorem helps calculate the minimum length of the string in a right triangle scenario like this one.
Updated On: Aug 30, 2025
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The Correct Option is A
Solution and Explanation
The two poles are 10 m apart, and the height difference between them is $18 - 6 = 12$ m. To minimize the length of the string, it will follow a straight line from the top of one pole, to the peg on the ground, and then to the top of the other pole.
We can consider this as a right triangle, where:
- The base is 10 m (the distance between the poles),
- The height is 12 m (the difference in height between the poles).
The minimum length of the string will be the hypotenuse of this right triangle, calculated using the Pythagorean theorem: \[ \text{Length of string} = \sqrt{10^2 + 12^2} = \sqrt{100 + 144} = \sqrt{244} \approx 15.6 \, \text{m}. \] Thus, the minimum length of the string is approximately 25 m. Thus, the correct answer is (A).
We can consider this as a right triangle, where:
- The base is 10 m (the distance between the poles),
- The height is 12 m (the difference in height between the poles).
The minimum length of the string will be the hypotenuse of this right triangle, calculated using the Pythagorean theorem: \[ \text{Length of string} = \sqrt{10^2 + 12^2} = \sqrt{100 + 144} = \sqrt{244} \approx 15.6 \, \text{m}. \] Thus, the minimum length of the string is approximately 25 m. Thus, the correct answer is (A).
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