Question

Which side lengths form a right triangle?

Answer 1

Answer: A and C

Step-by-step explanation: To see if it can be the side lengths of a right triangle we have to use the Pythagoras Theorem which is $a^2 +b^2 = c^2$

C is always the largest length. Now we can sub the numbers in

$5^2+\sqrt{6} ^2=\sqrt{31} ^2$

The squares and the square roots cancel each other out so we end up with

25+6=31

this is true so those are possible sides for a right triangle

Now for b:

$\sqrt{5}^2 + \sqrt{5}^2 =50^2$

Again the squares and square roots cancel each other out

5+5=2500

This isn't true so it isn't the possible sides for a right triangle

Finally option C:

$9^2+12^2=15^2$

81+144=225

225=225

This is true so it can be the side lengths that form a right triangle