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The question labeled **#8** in the image asks us to find the length of \( BC \) given the following:

- \( AC = 4 \)
- \( CD = 5 \)
- \( AB = 6 \)
- The perimeter of quadrilateral \( ABCD \) is 20.

Since the perimeter is the sum of all the side lengths, we can set up the equation:

\[
AB + BC + CD + DA = 20
\]

Given:
- \( AB = 6 \)
- \( CD = 5 \)
- \( AC = 4 \) (note that this is a diagonal, not a side of the quadrilateral)

Since \( DA \) is not explicitly given, we’ll assume the missing side is \( DA = x \). Thus:

\[
6 + BC + 5 + x = 20
\]

Simplifying, we find:
\[
BC + x = 9
\]

If we interpret this correctly based on the diagram or given values in context, let me know if it appears different. 

Would you like further steps or confirmation

Given AC = 4, CD = 5, and AB = 6 as in the diagram, find BC if the perimeter of ABCD is 20.

Learn how to find the missing side length BC in a quadrilateral ABCD given side lengths AC = 4, CD = 5, AB = 6, and a perimeter of 20. This problem involves key concepts in geometry and algebra, suitable for students in Grades 8-10.

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