To calculate the length of $PR$ using Pythagoras' Theorem, we need to understand the context of the triangle.

The Pythagorean theorem states: $a^2 + b^2 = c^2$ where:

• $a$ and $b$ are the lengths of the two legs (the sides that meet at a right angle), and
• $c$ is the length of the hypotenuse (the longest side of the right triangle).

In your case, the lengths given are:

• $PQ = 50 \, \text{cm}$,
• $QR = 48 \, \text{cm}$, and we are solving for $PR$, which is the hypotenuse.

Thus, applying the Pythagorean theorem: $PQ^2 + QR^2 = PR^2$ Substituting the known values: $50^2 + 48^2 = PR^2$ $2500 + 2304 = PR^2$ $4804 = PR^2$ Taking the square root of both sides: $PR = \sqrt{4804}$ $PR \approx 69.3 \, \text{cm}$

So, the length of $PR$ is approximately 69.3 cm (rounded to 1 decimal place).

Would you like further clarification or details on how this works?

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Here are some follow-up questions for you:

1. How do you apply Pythagoras' theorem in different types of triangles?
2. What would happen if the triangle was not a right-angled triangle?
3. How do you check if a triangle is a right-angled triangle?
4. What is the relationship between the lengths of the sides in an isosceles right triangle?
5. Can Pythagoras’ theorem be used in 3D geometry?

Tip: Remember, Pythagoras' theorem only works for right-angled triangles! Always verify if the triangle has a right angle before using it.