# PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR

**Solution:**

Reasoning:

It is given in the question that PQR is a right-angled triangle and it is right-angled at P.

So, we can apply the Pythagoras theorem here.

If it is right-angled at P then the side opposite to P will be the hypotenuse of the triangle i.e. QR and the other side is given PQ = 10cm and PR = 24.

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 QR.

For better visual understanding draw a right-angled triangle that is right-angled at Q and consider the side opposite to its PR as a hypotenuse

Given, PQ = 10 cm, PR = 24 cm and QR =?

By applying Pythagoras theorem in triangle PQR, we get (Hypotenuse)^{2 }= (Perpendicular)^{2 }+ (Base)^{2}

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

= (QR)^{2} = (10)^{2 }+ (24)^{2}

=(QR)^{2 }= 100 + 576

= (QR)^{2 }= 676

QR = 26 cm

Thus, QR is equal to 26 cm

Useful Tip:

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

**Video Solution:**

## PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR

### NCERT Solutions for Class 7 Maths - Chapter 6 Exercise 6.5 Question 1

PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR

QR is equal to 26 cm