SOLUTION: ABCD is a quadrilateral with AB=8, BC=13, and DC=15. What is the maximum possible integral value of AD?

Question 556147: ABCD is a quadrilateral with AB=8, BC=13, and DC=15. What is the maximum possible integral value of AD?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe the minimum integral value would be 11 and the maximum integral value would be 14.
here's why:
assume the left side of the quadrilateral is perpendicular to the top and bottom sides of the quadrilateral.
that's the shortest it can be.
now assume the right side of the quadrilateral is perpendicular to the top and bottom sides of the quadrilateral.
that's the shortest the right side can be which results in the longest the left side can be.
you would get a figure that looks like the following:
$$$$

the top figure is the shortest that the left side of the quadrilateral can be.
the bottom figure is the longest that the left side of the quadrilateral can be.

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