Question

determine if each set of numbers shown forms a pythagorean triple. a) {36, 77, 85} b) {21, 72, 80}

Explanation:

Step1: Recall Pythagorean theorem

For a set of three positive - integers \(a\), \(b\), \(c\) (where \(c\) is the largest), they form a Pythagorean triple if \(a^{2}+b^{2}=c^{2}\).

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

Calculate \(36^{2}+77^{2}\):
\(36^{2}=36\times36 = 1296\), \(77^{2}=77\times77 = 5929\). Then \(36^{2}+77^{2}=1296 + 5929=7225\). And \(85^{2}=85\times85 = 7225\). Since \(36^{2}+77^{2}=85^{2}\), \(\{36,77,85\}\) is a Pythagorean triple.

Step3: Check set (b) \(\{21,72,80\}\)

Calculate \(21^{2}+72^{2}\):
\(21^{2}=21\times21 = 441\), \(72^{2}=72\times72 = 5184\). Then \(21^{2}+72^{2}=441+5184 = 5625\). And \(80^{2}=80\times80 = 6400\). Since \(21^{2}+72^{2}
eq80^{2}\), \(\{21,72,80\}\) is not a Pythagorean triple.

Answer:

a) Yes
b) No