Question

A tree is broken at a height of 4m from the ground. Its top touches the ground at

a distance of 3m from the base of the tree. Find the original height of the tree.​

Answer 1

Given:-

• Tree broken at the height of 4m from the ground

• Top touches the ground at a distance of 3m from the base of the tree

To find:-

• Original height of the tree.

Let :-

• Part after breaking down be AB.
• Distance of its top from base if the tree be BC.

Therefore,

• AB = 4 m
• CB = 3 m
• To find AC = ?

By Pythagoras theorem,

$\mathtt{\implies{(AC)²= (AB)² + (BC)²}}$

$\mathtt{\implies{(AC)² = (4)²+(3)²}}$

$\mathtt{\implies{(AC)² = 16 +9}}$

$\mathtt{\implies{(AC)² = 25}}</p><p>$

$\mathtt{\implies{AC = \sqrt{25} }}</p><p>$

$\color{green}{ \large{\mathtt{\implies{AC = 5 \: cm}}}}</p><p>$

Original height of the tree :-

$\color{purple}{\large{\mathtt{\leadsto{AB+AC }}}}</strong></p><p><strong>\color{purple}$

$\color{purple}{\large{\mathtt{\leadsto{4 + 5}}}}</strong></p><p><strong>$

$\color{blue}{\boxed{\Large{\mathtt{\leadsto{9\: m}}}}}$

Therefore, original height of the tree Is 9m.