AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:

Correct Option (2)

The problem describes a scenario that forms a right-angled triangle. Let A be the base of the tree, C be the point where the trunk broke, and D be the point where the top of the broken part (B) touches the ground.

• The vertical portion of the trunk from the ground to the break point is AC = 12 meters.
• The horizontal distance from the base of the trunk (A) to where the broken part touches the ground (D) is AD = 5 meters.
• The broken part of the trunk, which was originally BC, now forms the hypotenuse CD of the right-angled triangle ACD. Therefore, BC = CD.
• Applying the Pythagorean theorem to triangle ACD: CD² = AC² + AD².
• Substituting the given values: CD² = 12² + 5².
• Calculation: CD² = 144 + 25 = 169.
• Therefore, CD = √169 = 13 meters.
• Since BC = CD, the length of the broken part is 13 meters.
• The original height of the trunk was the sum of the unbroken part (AC) and the broken part (BC).
• Original height = AC + BC = 12 m + 13 m = 25 meters.

Incorrect Options:

Options 1 (20 m), 3 (30 m), and 4 (35 m) are incorrect as they do not align with the calculation derived from the application of the Pythagorean theorem to the given dimensions. The only result consistent with the problem's parameters is 25 meters.