Side of a triangle

Question

In the figure, $AB=10\sqrt2$, $AC=11\sqrt2$ and $BC=12\sqrt2$.$DE$ and $BC$ are parallel and divides the triangle into two parts with equal area. What is the length of the line DE?

Answer 1

ADE and ABC are similar.And then using the fact that ratio of areas of two similar triangles is equal to the ratio of squares of their sides we get (DE/BC)^2 =1/2, which gives you DE=12.

Answer 2

A parallel line divides area as the square of corresponding sides of the similar triangles. I.e.,

$$ \dfrac {Area_{ADE}} {Area_{ABC} } = (DE/BC)^2 =\frac12 $$

So,

$$ DE = BC /\sqrt2 =12. $$