Question

On the portion of the straight line $x+y=2$ which is intercepted between the axes, a square is constructed, away from the origin, with this portion as one of its sides. If $p$ denotes the perpendicular distance of a side of this square from the origin, then the maximum value of $p$ is

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

Answer 1

Answer: (B)

$3\sqrt{2}$

Clearly $p=$ perpendicular distance from $(0,0)$ to $AD+$ side of the square
$=\frac{2}{\sqrt{2}}+2\sqrt{2}=3\sqrt{2}$