A tree is broken by the wind at a height from the foot. The broken upper part of 10 m length touches the ground at a distance of 6 m from the foot of the tree. Find the height of the tree.

Correct option is D

Given:

The length of the broken upper part of the tree = 10 meters.

The distance from the foot of the tree to the point where the upper part touches the ground = 6 meters.

Solution:

Let the height of the remaining part of the tree be $$h_1$$​, and the length of the broken part is 10 meters. Using the Pythagorean theorem:

​$$h_1^2 + 6^2 = 10^2$$​

​$$h_1^2 + 36 = 100$$​

​$$h_1^2 = 100 - 36 = 64$$

​$$h_1 = \sqrt{64} = 8 \text{ meters}$$​

Thus, the height of the remaining part of the tree is 8 meters.

The total height of the tree = height of the remaining part + length of the broken part:

Total height $$= h_1 + 10 = 8 + 10 = 18 \text{ meters}$$​