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

Step-by-step 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

Answer:

2,3,$\sqrt{13}$

Step-by-step explanation:

The first choice:

2, 3, $\sqrt{13}$

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 $\sqrt{13}$

So, 2² + 3² must be equal to ($\sqrt{13}$)²

Let's check if its true ...

2² + 3² = ($\sqrt{13}$)²

4 + 9 = 13

13 = 13

Right! Sides 2, 3, $\sqrt{13}$ are sides of a right triangle.

There is no need to check the other sets.