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The problem asks to find the length of side \( AD \) in the rectangle using Pythagoras' theorem. From the diagram:

- \( AB \) is the unknown side.
- \( BD \), the diagonal, is 5.3 cm.
- \( AD \), the height, is 4 cm.

Using the Pythagorean theorem:

\[
BD^2 = AB^2 + AD^2
\]

Substituting the known values:

\[
(5.3)^2 = AB^2 + (4)^2
\]
\[
28.09 = AB^2 + 16
\]
\[
AB^2 = 28.09 - 16 = 12.09
\]
\[
AB = \sqrt{12.09} \approx 3.48 \, \text{cm}
\]

So, the length of \( AB \) (which is \( AD \)) is approximately **3.48 cm**, rounded to 2 decimal places.

Do you want further details or have any questions?

Here are 5 related questions for further practice:
1. What would the length of side \( AB \) be if the diagonal was 6 cm and \( AD \) remained 4 cm?
2. How do you calculate the perimeter of the rectangle with the given dimensions?
3. What is the area of this rectangle based on the given lengths?
4. Can Pythagoras' theorem be used in non-right-angled triangles? Why or why not?
5. How would you find the length of the diagonal if only the lengths of \( AB \) and \( AD \) were given?

**Tip:** Always ensure your final answer is rounded to the required number of decimal places.

Use Pythagoras' theorem to work out the length of the side AD in the rectangle below. Give your answer in centimetres to 2 decimal places.

Use Pythagoras' theorem to calculate the length of side AD in a rectangle with a diagonal of 5.3 cm and height of 4 cm. Suitable for Grades 7-9 students learning geometry and right-angle triangles.

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