Question

which of the following sets of numbers could not represent the three sides of a right triangle? answer {36,77,85} {7,24,25} {24,45,51} {65,72,96}

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check \(\{36, 77, 85\}\)

\(36^2 + 77^2 = 1296 + 5929 = 7225\), \(85^2 = 7225\). So \(36^2 + 77^2 = 85^2\), valid.

Step3: Check \(\{7, 24, 25\}\)

\(7^2 + 24^2 = 49 + 576 = 625\), \(25^2 = 625\). So \(7^2 + 24^2 = 25^2\), valid.

Step4: Check \(\{24, 45, 51\}\)

\(24^2 + 45^2 = 576 + 2025 = 2601\), \(51^2 = 2601\). So \(24^2 + 45^2 = 51^2\), valid.

Step5: Check \(\{65, 72, 96\}\)

\(65^2 + 72^2 = 4225 + 5184 = 9409\), \(96^2 = 9216\). Since \(65^2 + 72^2
eq 96^2\), this set is invalid.

Answer:

\(\{65, 72, 96\}\)