To calculate the length of side $FG$ in the right triangle using Pythagoras' Theorem, we use the formula:

$c^2 = a^2 + b^2$

Here:

• $a = 9 \, \text{cm}$ (side $HF$),
• $b = 19 \, \text{cm}$ (side $HG$),
• $c$ is the hypotenuse (side $FG$).

Step-by-step calculation:

$FG^2 = HF^2 + HG^2$

$FG^2 = 9^2 + 19^2$

$FG^2 = 81 + 361 = 442$

Now, taking the square root of both sides:

$FG = \sqrt{442} \approx 21.0 \, \text{cm}$

So, the length of side $FG$ is approximately 21.0 cm, rounded to 1 decimal place.

Do you need further clarification or have any questions?

Here are some related questions to expand your understanding:

1. How would you calculate the length of $HG$ if only $FG$ and $HF$ were given?
2. Can you use the Pythagorean theorem in non-right triangles?
3. What is the general formula for finding the area of a right triangle?
4. How does the Pythagorean theorem relate to trigonometric ratios?
5. Can you determine the angle $H$ using the given sides?

Tip: Always check whether a triangle is right-angled before applying the Pythagorean theorem.