# A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 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. Let's visualize the situation as shown below.

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 5 m from the ground.

Suppose the tree is broken from R.

So, consider RQ as perpendicular and PR as the 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.

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.

**ā Check: **NCERT Solutions Class 7 Maths Chapter 6

**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

**Summary:**

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. The original height of the tree is 18 m.

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