Q. 135.0( 1 Vote )

In ΔABC, m∠

mB = 90

is a median

AE = EC

AC = 2AE

Applying Pythagoras Theorem :

AB2 + BC2 = AC2 …Equation (i)

Applying Appoloneous theorem

AB2 + BC2 = 2(AE2 + BE2)

AC2 = 2(AE2 + BE2)

Now since AC = 2AE

(2AE)2 = 2(AE2 + BE2)

2AE2 = 2BE2

AE = BE …Equation (ii)

AB2 + BC2 + AC2 = 2AC2 (From Equation (i))

AB2 + BC2 + AC2 = 2 × (2AE)2 = 8AE2

From Equation (ii) we can say that

AB2 + BC2 + AC2 = 8BE2

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