# Question #a86ed

Jul 26, 2016

See explanation.

#### Explanation:

If we assume that the side of the triangle is $a$ then we can write that:

• $A L = \frac{a \sqrt{3}}{2}$ - $A L$ is a height in an equilateral triangle.

• $C L = B L = \frac{a}{2}$ because $A L$ is also the bisector of the triangle's side $B C$

so $A {L}^{2} = \frac{3}{4} a$ and $B {L}^{2} = {a}^{2} / 4$, so $A {L}^{2} = 3 B {L}^{2}$

QED