Question

lee wants to build a right triangle. which of these sets of sides would not work? {44,24,50} {178,160,78} {159,84,135} {170,168,26}

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check set \(\{44,24,50\}\)

\(44^{2}+24^{2}=1936 + 576=2512\), \(50^{2}=2500\). Since \(44^{2}+24^{2}
eq50^{2}\).

Step3: Check set \(\{178,160,78\}\)

\(160^{2}+78^{2}=25600+6084 = 31684\), \(178^{2}=31684\). So \(160^{2}+78^{2}=178^{2}\).

Step4: Check set \(\{159,84,135\}\)

\(84^{2}+135^{2}=7056+18225 = 25281\), \(159^{2}=25281\). So \(84^{2}+135^{2}=159^{2}\).

Step5: Check set \(\{170,168,26\}\)

\(168^{2}+26^{2}=28224 + 676=28900\), \(170^{2}=28900\). So \(168^{2}+26^{2}=170^{2}\).

Answer:

\(\{44,24,50\}\)