Question

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

Answer 1

Given,

The tree is broken from the height $5m$.

Its top touches the ground at the distance of $12m$

By using the Pythagorean theorem we find the hypotenuse(broken piece).

Pythagorean theorem: $a^{2} +b^{2} =c^{2}$

Here $a=5m,b=12m$

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

$c^{2} =25+144\\c^{2} =169\\c=13$

Now to calculate original height of the tree we have to add the values $5,13$

$=5+13\\=18m$

Therefore, the original height of the tree is $18m$

Answer 2

Answer:

$18m$

Step-by-step explanation:

Given data,

• A tree is broken at a height $5m$ from the ground

• Its top touches ground at the distance of $12m$ base from the tree.
• As per the given data, height $=5m$ and base $=12m$.
• According to Pythogoras theorem

$Hypotenuse^{2} =height^{2}+base^{2}$

$\Rightarrow hypotenuse^{2}=5^{2} +12^{2}$

$\Rightarrow hypotenuse^{2}=25 +144$

$\Rightarrow hypotenuse^{2}=169$

$\Rightarrow hypotenuse=13m$

Now,

Original height of the tree

$=5+13$

$=18m$

Hence, the original height of the tree is $18m$.