# A tree is broken at a height of 5 m from the ground and its top touches the ground at 12 m from the base of the tree. Find the original height of the tree

**Solution:**

This question is based on the concept of the right-angled triangle and Pythagoras theorem.

Suppose P’Q is the height of the tree, as it is mentioned in the question that the tree is broken at a height of 5m from the ground.

Suppose the tree is broken from R.

So, consider RQ as perpendicular and PR as a broken part of the tree and, as the hypotenuse.

Remember, the length of PR that is broken part of the tree will remain the same as P'R.

Now, a right-angled triangle PQR is formed, apply the Pythagoras theorem, and find the length of the broken part that is PR.

As we must find out the original height of the tree for this, add the length of the broken part and the length where it broke that is QR.

For better visual understanding draw a right-angled triangle and visualize all the parts.

Let P'Q represents the original height of the tree before it broken at R and RP represents the broken part of the tree.

Triangle PQR is right-angled at Q. So, in this triangle, according to the Pythagoras theorem,

(Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}

(PR)^{2} = (RQ)^{2 }+ (PQ)^{2}

(PR)^{2} = (5)^{2 }+ (12)^{2}

(PR)^{2} = 25+144

(PR)^{2} = 169

PR = 13 m

Thus, the original height of the tree = PR + RQ

= 13 m + 5 m

= 18 m

The original height of the tree is 18 m.

Useful Tip:

Whenever you encounter a problem of this kind, it is best to think of the concept of a right-angled triangle.

**Video Solution:**

## A tree is broken at a height of 5 m from the ground and its top touches the ground at 12 m from the base of the tree. Find the original height of the tree

### NCERT Solutions for Class 7 Maths - Chapter 6 Exercise 6.5 Question 5

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

The original height of the tree is 18 m