Multiple choice

Directions : Answer the question independently. Two poles, one 78 m in height above the ground and the other 91 m in height above the ground, are at some distance from each other. Two strings are tied, one from the top of one pole to the bottom of the other and the other from the top of the second pole to the bottom of the first. Find the height (in m) above the ground at which the strings intersect. Assume strings are taut.

  1. 42m

  2. 50m

  3. 39 m

  4. Cannot be determined
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A Correct answer
Explanation

The height of intersection h for two poles of height h1 and h2 is given by the formula h = (h1 * h2) / (h1 + h2). Here, h = (78 * 91) / (78 + 91) = 7098 / 169 = 42 m.

AI explanation

For two poles of heights a and b, the height at which the intersecting strings cross is given by the formula ab divided by the quantity a plus b. Substituting the given heights of 78 m and 91 m, we calculate 78 times 91 divided by the sum of 78 and 91. The numerator is 7098 and the denominator is 169, which divides exactly to 42. Therefore, the strings intersect at a height of 42 m above the ground.

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