Question

in an equilateral triangle ABC,E is any point on BC such that BE=1 upon 4 BC.prove that 16 AE square = 13 AN square

Answer 1

AN?? where r u getting N

Answer 2

Answer:

oin 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 = 13AB²