In triangle ABC, angle C = 90 degrees, AC = 10cm and BC = 24cm. Calculate the length of AB.

From part 1(a), we found:

$$DE^2 + DF^2 = 144 \text{ cm}^2$$

From part 1(b), we found:

$$EF^2 = 144 \text{ cm}^2$$

We observe that $DE^2 + DF^2$ is equal to $EF^2$.

$$DE^2 + DF^2 = EF^2$$

Since the sum of the squares of two sides of $\triangle DEF$ is equal to the square of the third side, the triangle $\triangle DEF$ is a right-angled triangle. The right angle is opposite the side EF, which is the hypotenuse. Therefore, $\angle D = 90^\circ$.

You can conclude that $\triangle DEF \text{ is a right-angled triangle}$.