Question

lets try a cut out the
which set of sides would make a right triangle?

Explanation:

Step1: Apply Pythagorean theorem

For a set of sides \(a,b,c\) (\(c\) is the longest side), check if \(a^{2}+b^{2}=c^{2}\).
For \(8,10,12\): \(8^{2}+10^{2}=64 + 100=164\), \(12^{2}=144\), \(164
eq144\).
For \(5,12,13\): \(5^{2}+12^{2}=25+144 = 169\), \(13^{2}=169\).

Answer:

The set of sides \(5,12,13\) makes a right - triangle.