Multiple choice general knowledge math & puzzles

A cable, 16 meters in length, hangs between two pillars that are both 15 meters high. The ends of the cable are attached to the tops of the pillars. At its lowest point, the cable hangs 7 meters above the ground. The Question: How far are the two pillars apart?

  1. >16

  2. 0

  3. 16

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The cable is 16 meters long and hangs between two 15-meter pillars. Since the lowest point is 7 meters above the ground, the cable drops exactly 8 meters from the top of the pillars. Since the half-length of the cable is also 8 meters ($16/2$), the cable must hang completely vertically, folded in half. This means the two pillars must be 0 meters apart.

AI explanation

To solve this problem, we can use the concept of a right triangle and the Pythagorean theorem.

Let's assume that the distance between the two pillars is "x" meters.

We can form a right triangle with the cable as the hypotenuse, one pillar as the base, and the ground as the height. The other pillar will also have the same height.

Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can write the following equation:

$x^2 = 15^2 - 7^2$

$x^2 = 225 - 49$

$x^2 = 176$

Taking the square root of both sides, we get:

$x = \sqrt{176}$

$x \approx 13.26$

Therefore, the distance between the two pillars is approximately 13.26 meters.

Since none of the given options match the correct answer, we can conclude that the correct answer is D) None of these.

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