Question

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

Answer 1

Answer:

The original height of tree is 18 m.

Step-by-step explanation:

Consider the correct question is "A tree is broken at the height of 5m from the ground and its top touches the ground at a distance of 12m from the Base of the tree. Find the original height of the tree."

A tree is broken at the height of 5m from the ground.

Let the height of the tree is (x+5) m.

After broken, it will form a right angle triangle with hypotenuse x, base 12m and perpendicular 5 m.

Using Pythagoras theorem,

$hypotenuse^2=base^2+perpendicular^2$

$x^2=12^2+5^2$

$x^2=144+25$

$x^2=169$

Taking square root on both sides.

$x=13$

Height of tree = $x+5=13+5=18\text{ m}$

Hence, the height of tree is 18 m.

Answer 2

Answer:

18 cm.

Step-by-step explanation:

Please find the attachment.

Let ABC be the height of tree and tree is broken at point B such that top A touches the ground.

Now, we will use Pythagoras theorem to solve for length AB as AB is hypotenuse of right triangle.

$AB^2=BC^2+AC^2$

$AB^2=5^2+12^2$

$AB^2=25+144$

$AB^2=169$

Now, we will take positive square root of both sides as:

$\sqrt{AB^2}=\sqrt{169}$

$AB=13$

The total length of the tree would be $AB+BC\Rightarrow 13+5 =18$.

Therefore, the original height of the tree was 18 cm.