Answer
See below.
Work Step by Step
We have two side vectors $u$ and $v$ with two diagonals $d_1=u+v$ and $d_2=u-v$
Now, $|d_1|^2=|u|^2+|v|^2+2 u \cdot v$ and
$|d_2|^2=|u|^2+|v|^2 -2 u \cdot v$
and $|d_1|^2=|d_2|^2$
Then $2 u \cdot v-2 u \cdot v=0$
or, $|d_1|^2=|d_2|^2 \implies u \cdot v=0$
This means that $u \perp v$
Hence, the two sides will be perpendicular and the parallelogram must be a rectangle.
