Question 6 asks us to determine the length of the diagonal of a rectangle whose sides are 8 cm and 6 cm.

To find the length of the diagonal, we can use the Pythagorean theorem. For a rectangle, the diagonal forms a right triangle with the sides as the two legs. The formula is:

$d = \sqrt{l^2 + w^2}$

Where:

• $d$ is the diagonal,
• $l$ is the length (8 cm),
• $w$ is the width (6 cm).

Substituting the values:

$d = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{cm}.$

Thus, the length of the diagonal is 10 cm.

Would you like further details or clarifications on this?

Here are some related questions:

1. How do you derive the Pythagorean theorem?
2. What happens if the sides of the rectangle are unequal?
3. How do you calculate the area of the rectangle using the diagonal?
4. Can you apply the Pythagorean theorem in 3D geometry?
5. How does the diagonal change if the rectangle's sides are doubled?

Tip: The Pythagorean theorem can be applied in any right triangle to find the length of the hypotenuse, which is the diagonal in a rectangle.