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The question asks you to find the length of side \( AD \) in the rectangle, using Pythagoras' theorem. Here's the information given:

- \( BC = 4 \, \text{cm} \)
- Diagonal \( BD = 4.7 \, \text{cm} \)

Since \( BD \) is the diagonal of the rectangle, triangle \( ABD \) is a right-angled triangle. We can apply Pythagoras' theorem here:

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

Given that \( BD = 4.7 \, \text{cm} \) and \( AB = 4 \, \text{cm} \), we can now substitute these values into the equation to find \( AD \).

Let’s calculate this:

\[
(4.7)^2 = (4)^2 + AD^2
\]
\[
22.09 = 16 + AD^2
\]
\[
AD^2 = 22.09 - 16 = 6.09
\]
\[
AD = \sqrt{6.09} \approx 2.47 \, \text{cm}
\]

Thus, the length of side \( AD \) is approximately **2.47 cm** (to 2 decimal places).

Would you like further explanation on any step, or details about the Pythagorean theorem?

Here are 5 related questions:
1. How is the Pythagorean theorem applied in different shapes like triangles or polygons?
2. Can you explain why a rectangle always forms a right-angled triangle when divided by a diagonal?
3. How do you calculate the perimeter of a rectangle if only the diagonal and one side are given?
4. What is the relation between the diagonal and sides of a square compared to a rectangle?
5. How would the solution change if the given side \( BC \) were different?

**Tip:** Always ensure that you identify the right-angled triangle correctly when applying Pythagoras' theorem!

Use Pythagoras' theorem to work out the length of side AD in the rectangle. The diagonal BD is 4.7 cm, and side BC is 4 cm. Give your answer in centimetres to 2 decimal places.

Learn how to calculate the length of side AD in a rectangle using Pythagoras' theorem, given the diagonal BD is 4.7 cm and side BC is 4 cm. The solution includes key geometric concepts and is suitable for students in Grades 6-8.

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