8. ABCD is a rhombus. If side 
𝐵
𝐷
=
16
BD=16 cm and 
𝐴
𝐶
=
10
AC=10 cm, find 
𝐴
𝐶
AC.

It seems like you want to find the length of diagonal \( AC \) in the rhombus \( ABCD \). You have already provided the length of diagonal \( BD = 16 \) cm, and \( AC = 10 \) cm.

For a rhombus, the diagonals bisect each other at right angles. This means that the diagonals divide the rhombus into four right triangles. Each diagonal will be split in half, creating two segments for each diagonal.

In your case:
- \( BD = 16 \) cm, so half of \( BD \) is \( \frac{16}{2} = 8 \) cm.
- \( AC = 10 \) cm, so half of \( AC \) is \( \frac{10}{2} = 5 \) cm.

Now, since the diagonals are perpendicular, we can apply the Pythagorean theorem to one of the right triangles formed by the diagonals. The right triangle has legs of \( 8 \) cm (half of \( BD \)) and \( 5 \) cm (half of \( AC \)), and the hypotenuse is the side of the rhombus, \( AB \).

Using the Pythagorean theorem:

\[
AB^2 = 8^2 + 5^2
\]
\[
AB^2 = 64 + 25
\]
\[
AB^2 = 89
\]
\[
AB = \sqrt{89}
\]

Therefore, the side of the rhombus is \( AB = \sqrt{89} \) cm. 

Since all sides of a rhombus are equal, \( AB = BC = CD = DA = \sqrt{89} \) cm.

If you meant something else regarding the question, feel free to clarify.

Would you like me to explain any further steps or solve something else related to rhombuses or geometry in general?

Here are some related questions you might find helpful:
1. How do you prove that the diagonals of a rhombus are perpendicular?
2. What is the formula for the area of a rhombus given the diagonals?
3. How can you calculate the perimeter of a rhombus if you know the side length?
4. How do you use the Pythagorean theorem in other quadrilaterals?
5. What is the difference between a rhombus and a square?

**Tip:** When working with rhombuses, remember that the diagonals not only bisect each other but also divide the shape into four congruent right-angled triangles.

ABCD is a rhombus. If side BD = 16 cm and AC = 10 cm, find AC.

Learn how to find the side length of a rhombus using the lengths of its diagonals. Given BD = 16 cm and AC = 10 cm, this problem involves using the Pythagorean theorem to calculate the side length of the rhombus. Suitable for students in Grades 7-9.

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