Question

which of the following sets of numbers could be sides of a right triangle? select three correct answers. {36,84,76} {14,48,50} {36,11,34} {65,56,33} {96,110,146}

Explanation:

Step1: Apply Pythagorean theorem

For a set of numbers \(a,b,c\) (\(c\) is the largest number), check if \(a^{2}+b^{2}=c^{2}\).

For \(\{14,48,50\}\)

\(14^{2}+48^{2}=196 + 2304=2500\) and \(50^{2}=2500\).

For \(\{65,56,33\}\)

\(33^{2}+56^{2}=1089+3136 = 4225\) and \(65^{2}=4225\).

For \(\{96,110,146\}\)

\(96^{2}+110^{2}=9216+12100=21316\) and \(146^{2}=21316\).

For \(\{36,84,76\}\)

\(36^{2}+76^{2}=1296 + 5776=7072\) and \(84^{2}=7056
eq7072\).

For \(\{36,11,34\}\)

\(11^{2}+34^{2}=121+1156 = 1277\) and \(36^{2}=1296
eq1277\).

Answer:

B. \(\{14,48,50\}\), D. \(\{65,56,33\}\), E. \(\{96,110,146\}\)