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Age 14 to 16 Short Challenge Level:

Jack's teacher asked him to draw a triangle of area $7\textrm{ cm}^2$.
Two sides are to be of length $6\textrm{ cm}$ and $8\textrm{ cm}$.

How many possibilities are there for the length of the third side of the triangle?

If you liked this problem, here is an NRICH task that 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.