Question

Which of the following sets could be the sides of a right triangle? {2, 3,square root 10} {3, 5, square root 34} {5, 8, 12}

Answer 1

Answer:

Option 2 is correct.

Step-by-step explanation:

For right triangle

The pythagoras theorem should satisfy

The square of longest side should be equal to the sum of square of other two sides

$c^2=a^2+b^2$

Case1:

We have $(2,3,\sqrt{10})$

If we substitute in the formula

$c=\sqrt{10},a=2,b=3$  we get:

$10\neq9+2$

which does not satisfy the condition.

Case2:

We have  $(3,5,\sqrt{34})$

If we substitute in the formula

$c=\sqrt{34},a=3,b=5$  we get:

34=25+9

which satisfies the condition.

Hence, option 2 is correct.