QUESTION

CSAT

Hard

Maths

Prelims 2016

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

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Explanation

Given: AB is the original height of the tree. The broken part CB falls and touches the ground at D. The distance between point A and point D is 5 meters. The height of the tree at the breaking point is 12 meters. This forms a right triangle ACD with: AC = 12 meters (the height of the tree at the break). AD = 5 meters (distance from the base to the point where the broken part touches the ground).

CD = $\sqrt{AC^2 + AD^2}$ Calculation: CD = $\sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$ m