# 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°

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