Question

A tree is broken at a height of $5$ m from the ground and its top touches the ground at a distance of $12$ m from the base of the tree. Find the original height of the tree.

• A. $10m$
• B. $15m$
• C. $13m$
• D. $18m$

Answer 1

The correct option is D $18m$

Let $BD$ be the original height of tree.

$\therefore AD=AC$

In $△ABC$

$A{C}^2=A{B}^2=B{C}^2$

$=5^2+{12}^2$

$=169$

$=13\times 13$

$\Rightarrow AC=13m$

$\Rightarrow AD=13m$

$\therefore$ Original height of tree $=(13+5)m$

$=18m$