Question

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

Answer 1

In ∆PQR, PQ = √8 , QR = √5 , PR = √3

Longest side of ∆PQR = PQ = √8

∴ PQ² = (√8)² = 8

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

QR² + PR² = (√5)² + (√3)² = 5 + 3 = 8

∴ PQ² = QR² + PR²

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

by Converse of Pythagoras theorem,

∴ ∆PQR is a right-angled triangle.

Now, PQ is the hypotenuse.

∴ ∠PRQ = 90°        ...(Angle opposite to hypotenuse)

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