Q. 154.6( 8 Votes )

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

Answer :

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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