Question 1001777
Let's assume the gate is a rectangle.

Use Pythagorean theorem

{{{n^2 +(2n)^2 = 96^2}}}
{{{n^2 + 4n^2 = 9216}}}
{{{5n^2 = 9216}}}
{{{n^2 = 1843.2}}}
{{{n = 42.93}}} inches
The gate is approximately 42.93 inches by 85.86 inches