The two shorter sides of a right triangle have the same length. the area of the right triangle is 8.63 square meters. what is the length of the hypotenuse?

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

5.875 m

You would plot 83 on the 83 line and you would plot -113 on the -113 line.