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As Long as Possible

Age 11 to 14 Short
Challenge Level

The length of each side of a quadrilateral $ABCD$ is a whole number of centimetres. Given that $AB=4 \; \text{cm}$, $BC = 5 \; \text{cm}$ and $CD = 6 \; \text{cm}$, what is the maximum possible length of the fourth side $DA$?
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.