Question

A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke

Answer 1

Answer:

A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke?

The tree broke at height of 16 m

Step-by-step explanation:

Let's say that the tree broke at a height of x metres, then the rest of the height of the tree is 36 - x metres.

The tree broke in such a manner that it forms a right-angled triangle with the following dimensions, (the image attached):

x m

36 - x m

12 m

x meters as the height, (36-x) as the hypotenuse and 12 as the breadth.

We can use Pythagoras theorem to find x.

       x²   + 12² = (36 - x)²

       x²   + 144 = x² - 72x + 1296

       x² - x² + 72x = 1296 - 144

       72x = 1152

           x = 1152/72

           x =16

Therefore the tree broke at the height of 16 m.