Question

which of the following sets of numbers could represent the three sides of a right triangle? answer {20,21,28} {24,32,39} {31,60,68} {6,8,10}

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\) where \(c\) is the hypotenuse (longest side), \(a\) and \(b\) are the legs.

Step2: Check \(\{20,21,28\}\)

\(20^2 + 21^2 = 400 + 441 = 841\), \(28^2 = 784\). \(841
eq784\), so not a right triangle.

Step3: Check \(\{24,32,39\}\)

\(24^2 + 32^2 = 576 + 1024 = 1600\), \(39^2 = 1521\). \(1600
eq1521\), so not a right triangle.

Step4: Check \(\{31,60,68\}\)

\(31^2 + 60^2 = 961 + 3600 = 4561\), \(68^2 = 4624\). \(4561
eq4624\), so not a right triangle.

Step5: Check \(\{6,8,10\}\)

\(6^2 + 8^2 = 36 + 64 = 100\), \(10^2 = 100\). \(100 = 100\), so it satisfies the Pythagorean theorem.

Answer:

\(\{6, 8, 10\}\)