Question

Can anyone answer this ?

Answer 1

For this case we have that by definition, the Pythagorean theorem states that:

$c = \sqrt {a ^ 2 + b ^ 2}$

Where:

c: It is the hypotenuse of the triangle

a, b: They are the legs of the triangle

Then, we verify if the theorem for the given triangles is fulfilled:

Triangle 1:

$\sqrt {13} = \sqrt {2 ^ 2 + 3 ^ 2}\\\sqrt {13} = \sqrt {4 + 9}\\\sqrt {13} = \sqrt {13}$

It is fulfilled!

Triangle 2:

$25 = \sqrt {2 ^ 2 + (3 \sqrt {2}) ^ 2}\\25 = \sqrt {4+ (9 * 2)}\\25 = \sqrt {22}$

It is not fulfilled!

Triangle 3:

$43 = \sqrt {2 ^ 2 + (3 \sqrt {3}) ^ 2}\\43 = \sqrt {4+ (9 * 3)}\\43 = \sqrt {4+ (9 * 3)}\\43 = \sqrt {31}$

It is not fulfilled!

ANswer:

Triangle A