NRICH: Third Side

What are the possible lengths for the third side of this right-angled triangle?

The lengths of the sides of a right-angled triangle are all integers.

The sum of the lengths of the hypotenuse and one of the other sides is 49.

What are the three possible lengths for the third side?

This problem is adapted from theĀ World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in ourĀ short problems collection.

Age 14 to 16


Algebra & Pre-Algebra, Geometry, Quadratic Equations
High School

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