In the figure PQ = 24cm, QR = 26 cm, ∠PAR =90°, PA = 6 cm and AR =8cm . Find angle QPR.

We have

Given: PQ = 24 cm

QR = 26 cm

PA = 6 cm

AR = 8 cm

∠PAR = 90°

We need to find ∠QPR.

We know that ∆PAR is a right-angled triangle, right angled at A.

So, by Pythagoras theorem, we can write as

PR² = PA² + AR²

⇒ PR² = 6² + 8²

⇒ PR² = 36 + 64

⇒ PR² = 100

⇒ PR = √100

⇒ PR = 10

Now, in ∆PQR apply Pythagoras theorem again,

PQ² + PR² = 24² + 10²

PQ² + PR² = 576 + 100 = 676

But QR² = 26² = 676 [∵ QR = 26 cm]

⇒ PQ² + PR² = QR²

Therefore, by the converse of Pythagoras theorem

∠P = 90°

⇒ ∠QPR = 90°