Question

In ∆PQR, PQ = √8 , QR = √5 , PR = √3 . Is ∆PQR a right angled triangle? If yes, which angle is of 90°?

Answer 1

. 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°.