Question

The top of a broken tree touches the ground at a distance of $12m$ from its base. If the tree is broken at a height of $5m$ from the ground then the actual height of the tree is

• A. $25m$
• B. $13m$
• C. $18m$
• D. $17m$

Answer 1

Answer: (C)

Let $AB$ is the unbroken part of the tree and $BC$ is the broken part of it.

Hence, we form the following diagram.

Since, after broken top of the tree $\left(C\right)$ touches the ground at $12m$ distance from the foot of the point $\left(A\right)$ of the tree.

Here, triangle $ABC$ is right-angled triangle.

$AC$ is the distance between feet of the tree and top of the tree.

Recall the Pythagoras theorem,

In a right angles triangle the square of the hypotenuse is equal to the sum of the squares of other two sides.

$\Rightarrow \text{In}\Delta ABC,(BC{)}^2=(AB{)}^2+(AC{)}^2$
$\Rightarrow (BC{)}^2=5^2+{12}^2$
$\Rightarrow (BC{)}^2=25+144$
$\Rightarrow (BC{)}^2=169$
$\Rightarrow (BC{)}^2=13m$
Now actual height of tree $=AB+BC$
$=5m+13m$
$=18m$

Therefore, the actual height of the tree is $18m$.

Hence, Option B is correct.