Question

In quadrilateral ABCD, we have AB=3, BC=6, CD=4, and DA=4.

If the length of diagonal AC is an integer, what are all the possible values for AC?

With a full explanation please.

Answer 1

"4, 5, 6, 7"

Copy and Paste these into your answer without the quotation marks.

Answer 2

The triangle inequality applies.

In order for ACD to be a triangle, AC must lie between CD-DA=0 and CD+DA=8.

In order for ABD to be a triangle, AC must lie between BC-AB=3 and BC+AB=9.

The values common to both these restrictions are numbers between 3 and 8. Assuming we don't want the diagonal to be coincident with any sides, its integer length will be one of ...
{4, 5, 6, 7}