Question

The $ABCD$ is a square with sides of unit length. Points $E$ and $F$ are taken on sides $AB$ and $AD$ respectively so that $AE=AF$. Let $P$ be a point inside the square $ABCD$.
Let a line passing through point $A$ divides the square $ABCD$ into two parts so that area of one portion is double the other, then the length of portion of line inside the square is

• A. $\frac{\sqrt{10}}{3}$
• B. $\frac{\sqrt{13}}{3}$
• C. $\frac{\sqrt{11}}{3}$
• D. $\frac{2}{\sqrt{3}}$

Answer 1

Answer: (B)

$\frac{1}{2}y\cdot (1)=\frac{1}{3}\cdot (1);$
$y=\frac{2}{3}$

$L_{AQ}=\sqrt{(1{)}^2+{\left(\frac{2}{3}\right)}^2}=\frac{\sqrt{13}}{3}$