Right Triangle Problem: Calculate Side Length Using Height 10cm and Area 40cm²

To solve this problem, we will find the length of side DF using the formula for the area of a triangle:

The area of a triangle is given by:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

For triangle DEF, the area is given as 40 cm², and the height GE is 10 cm. We can consider side DF as the base. Therefore, substitute the given values:
$\frac{1}{2} \times \text{DF} \times 10 = 40$

Simplify this expression:
$\text{DF} \times 5 = 40$

Divide both sides by 5 to solve for DF:
$\text{DF} = \frac{40}{5} = 8$

Thus, the length of side DF is $\text{8 cm}$.

By comparing with the given choices, the correct answer is indeed choice 1, which is 8 cm.

Therefore, the solution to the problem is $\text{8 cm}$.