Question

A tree of height 36m is on one edge of a road of width 12m. it falls such that the top of the tree touches the other edge of the road. find the height at which the tree breaks.

a.16

b.24

c.12

d.18

Answer 1

Please see the attached file.

According to the figure,

(36-h)^2=h^2+12^2

Solving we get,

h=16

Thus, the tree breaks at the height of 16m

Therefore, option (a) is correct.

Answer 2

Given :

A tree of height 36m is on one edge of a road of width 12m. it falls such that the top of the tree touches the other edge of the road.

To Find :

Find the height at which the tree breaks.

Solution:

Refer the attached figure

Height of tree AB = 36 m

Width of road BC = 12 m

It falls such that the top of the tree touches the other edge of the road.

Let E be the point at which the tree breaks

Let BE be x

So, AE = 36-x

So, AE = EC = 36-x

Now we will use Pythagoras theorem

$Hypotenuse^2 =Perpendicular^2+base^2\\(36-x)^2=x^2+12^2\\36^2+x^2-72x=x^2+144\\36^2-72x=144\\36^2-144=72x\\\frac{36^2-144}{72}=x\\16=x$

So, BE = 16 m

So,  the height at which the tree breaks is 16 m