Question

In a equilateral triangle, prove that three times the square of one of its altitudes.

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

△ABC is an Equilateral Triangle.

AB=BC=AC

CD Perpendicular to AB

To Prove:

3AC2=4CD2

Proof:

In △ADC

By Pythagoras Theorem,

AC2=AD2+DC2.....(1)

In △BDC

By Pythagoras Theorem,

BC2=DC2+BD2.....(2)

Adding 1) and 2) We get,

2AC2=2DC2+AD2+BD2 (SinceAC=BC)

Since, AD=BD=21AC (SinceAC=AB)

∴ 2AC2=2DC2+21AC2

∴ 2AC2−21AC2=2DC2

∴ 3AC2=4CD2