Question

which of the following sets of numbers could not represent the three sides of a right triangle? answer {12,16,20} {36,77,85} {48,65,80} {57,76,95}

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) is the hypotenuse), \(a^{2}+b^{2}=c^{2}\).

Step2: Check the set \(\{12,16,20\}\)

\(12^{2}+16^{2}=144 + 256=400\), and \(20^{2}=400\). So \(12^{2}+16^{2}=20^{2}\).

Step3: Check the set \(\{36,77,85\}\)

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

Step4: Check the set \(\{48,65,80\}\)

\(48^{2}+65^{2}=2304 + 4225=6529\), and \(80^{2}=6400\). Since \(48^{2}+65^{2}
eq80^{2}\).

Step5: Check the set \(\{57,76,95\}\)

\(57^{2}+76^{2}=3249+5776 = 9025\), and \(95^{2}=9025\). So \(57^{2}+76^{2}=95^{2}\).

Answer:

\(\{48,65,80\}\)