Question

Which of the following sets could be the sides of a right triangle?

{2,3, square root 13} {2,2,4}{1,3, square root 3}

Answer 1

Answer: 2, 3, square root 13

Explanation:

Use the Pythagorean Theorem (a^2 + b^2 = c^2)

2^2 = 4

3^2 = 9

4 + 9 = 13

Square root of 13 is c

Answer 2

2,3,
`√(13)`

Explanation:

The first choice:

2, 3,
`√(13)`

Pythagorean theorem states that for a right-triangle of sides a,b and c where c is the hypotenuse; a² + b² = c²

So the hypotunese has to be the longest side of all.

The longest side in this case is
`√(13)`

So, 2² + 3² must be equal to (
`√(13)`)²

Let's check if its true ...

2² + 3² = (
`√(13)`)²

4 + 9 = 13

13 = 13

Right! Sides 2, 3,
`√(13)` are sides of a right triangle.

There is no need to check the other sets.