Question

If PQ = 2m, QR = m² – 1 and PR = m² + 1, show that PQR is a right-angled triangle. Hence, find the sides of triangle when m = 4, 5, 6.

Answer 1

Given, PQ = 2m, QR = m² – 1 and PR = m² + 1

Let’s take m to be 4.

⇒ 2m = 2 × 4 = 8

⇒ m² – 1 

= 4² – 1

= 16 – 1

= 15

⇒ m² + 1

= 4² + 1

= 16 + 1

= 17

Let’s take m to be 5.

⇒ 2m = 2 × 5 = 10

⇒ m² – 1

= 5² – 1

= 25 – 1

= 24

⇒ m² + 1

= 5² + 1

= 25 + 1

= 26

Finally, take m to be 6.

⇒ 2m = 2 × 6 = 12

⇒ m² – 1

= 6² – 1

= 36 – 1

= 35

⇒ m² + 1

= 6² + 1

= 36 + 1

= 37

Hence, the required is (8, 15, 17), (10, 24, 26) and (12, 35, 37).