Question

In an equilateral traingle ABC, E is any point on BC such that BE=1/4BC. Prove that 16 AE2=13AB2

Answer 1

Answer:

Step-by-step explanation:

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

Hope that this answer will help you ✌️

Answer 2

this one is like the one in NCERT.. but seems even better.. nice question..