Question

which of the following sets of numbers could represent the three sides of a right triangle?
answer
{9,12,15} {10,23,26}
{22,28,35} {30,40,51}

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 \(\{9,12,15\}\)

\(9^2 + 12^2 = 81 + 144 = 225\), \(15^2 = 225\). So \(9^2 + 12^2 = 15^2\).

Step3: Check \(\{10,23,26\}\)

\(10^2 + 23^2 = 100 + 529 = 629\), \(26^2 = 676\). \(629
eq676\).

Step4: Check \(\{22,28,35\}\)

\(22^2 + 28^2 = 484 + 784 = 1268\), \(35^2 = 1225\). \(1268
eq1225\).

Step5: Check \(\{30,40,51\}\)

\(30^2 + 40^2 = 900 + 1600 = 2500\), \(51^2 = 2601\). \(2500
eq2601\).

Answer:

\(\{9, 12, 15\}\)