# ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC

**Solution:**

This question is straightforward, as it is given in the question that ABC is a triangle, right-angled at C.

So, we can apply the Pythagoras theorem here, if it is right-angled at C then the side opposite to C will be the hypotenuse of the triangle that is AB = 25 cm, and the other two sides are AC = 7 cm and BC.

Now, by applying the Pythagoras theorem i.e. in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides, we can find BC.

For better visual understanding draw a right-angled triangle that is right-angled at C and consider the side opposite to it AB as the hypotenuse

Given, ABC is a triangle which is right-angled at C. AB = 25cm, AC = 7 cm and BC =?

In triangle ACB, By Pythagoras theorem, (Hypotenuse)^{2} = (Perpendicular)^{2 }+ (Base)^{2}

= (AB)^{2 }= (AC)^{2 }+ (BC)^{2}

= (25)^{2} = (7)^{2 }+ (BC)^{2}

625 = 49 + (BC)^{2}

(BC)^{2 }= 625 – 49

(BC)^{2} = 576

BC = 24 cm

Thus, BC is equal to 24cm

Useful Tip

Whenever you encounter problems of this kind, it is best to think of the Pythagoras theorem for the right-angled triangle.

**Video Solution:**

## ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC

### NCERT Solutions for Class 7 Maths - Chapter 6 Exercise 6.5 Question 2

ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC

BC is equal to 24cm