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in Pythagoras Theorem by (47.6k points)
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In ∆PQR, PQ = √8 , QR = √5 , PR = √3 . Is ∆PQR a right angled triangle? If yes, which angle is of 90°?

1 Answer

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Best answer

. Longest side of ∆PQR = PQ = √8

∴ PQ2 = (√8)2 = 8 

Now, sum of the squares of the remaining sides is,

QR2 + PR2 = (√5)2 + (√3)2 

= 5 + 3 

= 8 

∴ PQ2 = QR2 + PR2 

∴ Square of the longest side is equal to the sum of the squares of the remaining two sides. 

∴ ∆PQR is a right-angled triangle. [Converse of Pythagoras theorem]

Now, PQ is the hypotenuse. 

∴∠PRQ = 90° [Angle opposite to hypotenuse] 

∴ ∆PQR is a right-angled triangle in which ∠PRQ is of 90°.

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