Triple Pythagoras

Can you work out the length of the diagonal of the cuboid?

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Problem



 

Image
Triple Pythagoras



The diagram shows a cuboid.

In triangle XYZ, the lengths of XY, XZ and YZ are 9, 8 and $\sqrt{55}$ respectively.

What is the length of the diagonal XA?

This problem is taken from the UKMT Mathematical Challenges.