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!