MathNet 1997 — Part 01 Question 58

Question 58

Let a square $ABCD$ of unit side be given and let $M, N$ be two points respectively on the sides $AB$ and $AD$ such that $AM = AN$. What is the maximum value of the area of the quadrilateral $CDNM$?

$\frac{1}{2}$
$\frac{9}{16}$
$\frac{19}{32}$
$\frac{5}{8}$
$\frac{2}{3}$