Isosceles Right Triangle:
An isosceles right triangle is a triangle that has two sides of equal length and one right angle (90 degrees).

Properties of an Isosceles Right Triangle:
1. The two legs of an isosceles right triangle are congruent.
2. The hypotenuse of an isosceles right triangle can be found using the Pythagorean theorem.

Finding the Hypotenuse:
To find the length of the hypotenuse of an isosceles right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's assume that the length of each leg of the isosceles right triangle is 'x'. Since the triangle is isosceles, both legs are equal.

Applying the Pythagorean theorem:
Using the Pythagorean theorem, we have:
x^2 + x^2 = h^2
2x^2 = h^2

Finding the Area:
The area of a triangle is given by:
Area = 1/2 * base * height

Since the triangle is isosceles, the base and height are equal. Let's assume the base and height are both 'y'.

Applying the Area Formula:
Using the area formula, we have:
Area = 1/2 * y * y
8 = 1/2 * y^2
16 = y^2
y = 4

So, the base and height of the triangle are both 4 cm.

Finding the Hypotenuse (continued):
Substituting the value of 'y' in the equation for the hypotenuse, we have:
2x^2 = h^2
2(4)^2 = h^2
32 = h^2

Taking the square root of both sides, we find:
h = √32
h = 4√2

Therefore, the length of the hypotenuse of the isosceles right triangle is 4√2 cm.

Summary:
- An isosceles right triangle has two sides of equal length and one right angle.
- The hypotenuse of an isosceles right triangle can be found using the Pythagorean theorem.
- By assuming the length of the legs and applying the Pythagorean theorem, we can find the length of the hypotenuse.
- In this case, the length of the hypotenuse is 4√2 cm.