The problem asks for the length of a side of an isosceles right triangle, given that its area is $8 \, \text{m}^2$.

Solution:

1. Formula for the area of an isosceles right triangle: In an isosceles right triangle, the legs are of equal length, say $a$. The formula for the area of a triangle is: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ Since the base and height are both $a$ (because the triangle is isosceles), the area is: $\text{Area} = \frac{1}{2} \times a \times a = \frac{a^2}{2}$

2. Setting up the equation: We are given that the area is $8 \, \text{m}^2$. Therefore, we can set up the equation: $\frac{a^2}{2} = 8$

3. Solving for $a$: Multiply both sides by 2 to eliminate the fraction: $a^2 = 16$ Take the square root of both sides: $a = 4$

Thus, the length of each side of the triangle is 4 meters.

The correct answer is 04.

Would you like any more details or have any further questions on this problem?

Here are five related questions to consider:

1. What is the relationship between the sides of an isosceles right triangle and its hypotenuse?
2. How do you calculate the perimeter of this isosceles right triangle?
3. If the area were doubled, what would the new side length be?
4. How would the formula change if the triangle were not isosceles?
5. What is the hypotenuse of this triangle, given the side length?

Tip: For isosceles right triangles, the legs are equal, and the hypotenuse can be found using the Pythagorean theorem: $\text{hypotenuse} = a\sqrt{2}$.