Question

A side of an isosceles right angled triangle is x. Find its hypotenuse.

Answer 1

Let ∆PQR be the given right-angled isosceles triangle. 

PQ = QR = x.

In ∆PQR, ∠Q = 90° [Pythagoras theorem] 

∴ PR² = PQ² + QR² 

= x² + x² 

= 2x² 

∴ PR = \(\sqrt {2x^2}\) [Taking square root of both sides] 

= x\(\sqrt {2}\) units 

∴ The hypotenuse of the right-angled isosceles triangle is x\(\sqrt {2}\) units. 

∴ The hypotenuse of the right-angled isosceles triangle is x\(\sqrt {2}\) units.