Question

determine if each of the following sets of numbers could or could not make a right triangle. select the correct option for each set of numbers. numbers right triangle not a right triangle {37,77,86} {37,35,12} {48,54,72}

Explanation:

Step1: Apply Pythagorean theorem for \(\{37,77,86\}\)

Check if \(37^{2}+77^{2}=86^{2}\).
\(37^{2}=1369\), \(77^{2}=5929\), \(86^{2}=7396\).
\(1369 + 5929=7298
eq7396\).

Step2: Apply Pythagorean theorem for \(\{37,35,12\}\)

Check if \(12^{2}+35^{2}=37^{2}\).
\(12^{2}=144\), \(35^{2}=1225\), \(37^{2}=1369\).
\(144+1225 = 1369\).

Step3: Apply Pythagorean theorem for \(\{48,54,72\}\)

Check if \(48^{2}+54^{2}=72^{2}\).
\(48^{2}=2304\), \(54^{2}=2916\), \(72^{2}=5184\).
\(2304+2916=5220
eq5184\).

Answer:

• For \(\{37,77,86\}\): Not a Right Triangle
• For \(\{37,35,12\}\): Right Triangle
• For \(\{48,54,72\}\): Not a Right Triangle