Question 93
The side lengths of a parallelogram are $a$, $b$ and diagonals have lengths $x$ and $y$. Knowing that $a b = \frac{x y}{2}$, show that
$$
a = \frac{x}{\sqrt{2}},\ b = \frac{y}{\sqrt{2}} \quad \text{or} \quad a = \frac{y}{\sqrt{2}},\ b = \frac{x}{\sqrt{2}}
$$
$$
a = \frac{x}{\sqrt{2}},\ b = \frac{y}{\sqrt{2}} \quad \text{or} \quad a = \frac{y}{\sqrt{2}},\ b = \frac{x}{\sqrt{2}}
$$