Question

In an eq.triangle abc,E is a point on bc such that be=1/4 of bc.prove that 16ab^2=13ab^2

Answer 1

Heya Mate.....................

Here is your solution..............................

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Plz see Attachment file for the answer..............

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Thanks.............

Answer 2

Hello here is ur answer to your question ===============================

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Join A to mid-point of BC at D. Hence ED = BE = (1/4)BC --(1)

In triangle AED, AE² = AD² + ED² -----------------(2)

In triangle ABD, AD²  = AB² - BD²   --------------(3)

Putting value of AD² from (3) into (2),

AE² = AB² - BD² + ED² = AB² - (BC/2)² + (BC/4)²

as BD = (1/2)BC and ED = (1/4)BC from (1).

OR AE² = AB² - (AB/2)² + (AB/4)² as BC = AB as triangle ABC is equilateral.

Simplifying this , 16AE² = 13 ab^²