Question

which set of sides would make a right triangle? 8,10,12 5,10,12 4,5,6 5,12,13

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check the first set \(8,10,12\)

\(8^{2}+10^{2}=64 + 100=164\), \(12^{2}=144\), since \(164
eq144\), it's not a right - triangle.

Step3: Check the second set \(5,10,12\)

\(5^{2}+10^{2}=25 + 100 = 125\), \(12^{2}=144\), since \(125
eq144\), it's not a right - triangle.

Step4: Check the third set \(4,5,6\)

\(4^{2}+5^{2}=16 + 25=41\), \(6^{2}=36\), since \(41
eq36\), it's not a right - triangle.

Step5: Check the fourth set \(5,12,13\)

\(5^{2}+12^{2}=25+144 = 169\), \(13^{2}=169\), since \(5^{2}+12^{2}=13^{2}\), it is a right - triangle.

Answer:

5,12,13