∠A is right angle in ΔABC. AD is an altitude of the triangle. If AB = √5, BD = 2, find the length of the hypotenuse of the triangle.

m∠A = 90

AB = √5

BD = 2

Applying Pythagoras theorem in ΔADB we get

AD² = AB² – BD²

⇒ AD² = 5 – 4 = 1

⇒ AD = 1

Let AC = x

Applying Pythagoras theorem in ΔADC we get

DC² = AC² – AD²

⇒ DC² = x² – 1

⇒ DC = √(x² – 1)

Applying Pythagoras theorem in ΔABC we get

AB² + AC² = BC²

⇒ 5 + x² = (2 + √(x² – 1))²

⇒ 5 + x² = 4 + x² – 1 + 4√(x² – 1)

Hypotenuse BC = BD + DC

⇒ Hypotenuse BC