Question

which set of side lengths form a right triangle? 33, 56, 65 3, 4, 7 10, 15, 25 66, 72, 97

Explanation:

Step1: Apply Pythagorean theorem

For a set of side lengths \(a\), \(b\), \(c\) (\(c\) is the longest side), check if \(a^{2}+b^{2}=c^{2}\).
For \(33\), \(56\), \(65\):
\(33^{2}+56^{2}=1089 + 3136=4225\)
\(65^{2}=4225\)

Step2: Check other sets

For \(3\), \(4\), \(7\): \(3^{2}+4^{2}=9 + 16 = 25
eq7^{2}=49\)
For \(10\), \(15\), \(25\): \(10^{2}+15^{2}=100+225 = 325
eq25^{2}=625\)
For \(66\), \(72\), \(97\): \(66^{2}+72^{2}=4356+5184 = 9540
eq97^{2}=9409\)

Answer:

\(33,56,65\)