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

2
by karthik2000

Log in to add a comment

by karthik2000

Log in to add a comment

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