Question

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

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.

Step2: Check 33, 56, 65

\(33^{2}+56^{2}=1089 + 3136=4225\) and \(65^{2}=4225\). So \(33^{2}+56^{2}=65^{2}\).

Step3: Check 3, 4, 7

\(3^{2}+4^{2}=9 + 16=25\) and \(7^{2}=49\). Since \(25
eq49\), it's not a right - triangle.

Step4: Check 66, 72, 97

\(66^{2}+72^{2}=4356+5184 = 9540\) and \(97^{2}=9409\). Since \(9540
eq9409\), it's not a right - triangle.

Step5: Check 10, 15, 25

\(10^{2}+15^{2}=100 + 225=325\) and \(25^{2}=625\). Since \(325
eq625\), it's not a right - triangle.

Answer:

33, 56, 65