Find the length of altitude AD of an isosceles triangle ABC in which AB = AC = 2a units and BC = a units.​

An isosceles triangle ABC.

Two sides are equal i.e AB = AC = 2a.

Length of BC is a units.

What is the length of altitude AD ?

Let the length of altitude be x units. We have

AB = AC = 2a (hypotenuse)

AD = x (perpendicular)

BC = a

BD = DC = a/2 (base)

Now applying Pythagoras Theorem in ∆ADB

★ Hypotenuse² = P² + B² ★

⟹ AB² = AD² + BD²

⟹ 2a² = x² + (a/2)²

⟹ 4a² = x² + a²/4

⟹ 4a² – a²/4 = x²

⟹ 16a² – a²/4 = x²

⟹ √15a²/4 = x

⟹ a√15/2 = x

Hence, the length of altitude of isosceles triangle ABC is a√15/2 units.

a√15/2 units

Explanation:

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