Question

In an equilateral triangle ABC ,E is a point on BC such that BE=1/4BC. Prove that 16AE^2 = 13AB^2 .

Answer 1

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Answer 2

Answer: Join A to mid-point of BC at D. So,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)....,,,

So we get ....16AE² = 13AB²

Step-by-step explanation: