Because the two shorter sides of the right triangle are equal, it is an isosceles right triangle, wth angles 45°, 45° and 90°.
Let x = the length of one of the shorter sides, and
y = the length of the hypotenuse.
The area is 8.63 m², therefore
(1/2)x² = 8.63
x² = 17.26
From the Pythagorean Theorem, obtain
y² = x² + x² = 34.52
y = 5.875 m
Answer: 5.875 m