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In quadrilateral ABCD, we have AB = 3, BC = 6, CD = \(9\), and DA = \(12\).
If the length of diagonal AC is an integer, what are all the possible values for AC? Explain your answer in complete sentences.

 May 15, 2022
 #1
avatar+9457 
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The exact same problem was answered here: https://web2.0calc.com/questions/quadrilateral_18#r1

 May 15, 2022
 #2
avatar+1713 
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Notice that hte diagonal dorms 2 triangles, 1 with sides 3 and 6, and the other with 9 and 12. 

 

The triangle inequality states that the sum of the 2 smallest sides must be greater than the largest side. 

 

The only numbers that satisfy both triangles are \(\color{brown}\boxed{4,5,6,7,8}\)

 May 15, 2022

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