To solve for the length of $PR$ using Pythagoras' theorem, we use the formula:

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

Where $c$ is the hypotenuse (the longest side of the right triangle, $PQ$), and $a$ and $b$ are the other two sides ($PR$ and $RQ$).

Given:

• Hypotenuse ($PQ$) = $39 \, \text{cm}$
• One side ($RQ$) = $36 \, \text{cm}$

We need to find $PR$. Rearranging the formula:

$a^2 = c^2 - b^2$

Substituting the known values:

$PR^2 = 39^2 - 36^2$

$PR^2 = 1521 - 1296$

$PR^2 = 225$

$PR = \sqrt{225} = 15$

Final Answer:

The length of $PR$ is $15.0 \, \text{cm}$ (to 1 decimal place).

Would you like a detailed explanation of any step?

Here are 5 related questions:

1. How is Pythagoras' theorem applicable to other types of triangles?
2. How do we know which side of the triangle is the hypotenuse?
3. Can Pythagoras' theorem be used for 3D geometry problems?
4. How do we calculate a missing side if only the hypotenuse is given?
5. How does rounding impact the accuracy of answers in geometry?

Tip: Always double-check units and rounding instructions for accuracy in mathematical problems!