Finding the Length of the Hypotenuse of an Isosceles Right Triangle
An isosceles right triangle is a triangle with two sides of equal length and a right angle. In this case, we are given that the area of the triangle is 8 cm^2.

Area of a Triangle Formula:
The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Isosceles Right Triangle:
In an isosceles right triangle, the base and height are equal, so we can rewrite the formula as: Area = 1/2 * s^2, where s is the length of the base (which is also the height).

Given Information:
Area = 8 cm^2

Calculating the Length of the Base (s):
Using the formula for the area of a triangle, we can find the length of the base of the isosceles right triangle:
8 = 1/2 * s^2
16 = s^2
s = √16
s = 4 cm

Calculating the Length of the Hypotenuse:
In a right triangle, the hypotenuse can be found using the Pythagorean theorem: a^2 + b^2 = c^2, where c is the length of the hypotenuse.
Since the triangle is isosceles, the base and height are equal, so we have two legs of length 4 cm each. Let's denote one leg as a and the other leg as b:
a = 4 cm
b = 4 cm
Substitute the values into the Pythagorean theorem:
4^2 + 4^2 = c^2
16 + 16 = c^2
32 = c^2
c = √32
c ≈ 5.66 cm
Therefore, the length of the hypotenuse of the isosceles right triangle is approximately 5.66 cm.