For this case we have that by definition, the Pythagorean theorem states that:
[tex]c = \sqrt {a ^ 2 + b ^ 2}[/tex]
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:
[tex]\sqrt {13} = \sqrt {2 ^ 2 + 3 ^ 2}\\\sqrt {13} = \sqrt {4 + 9}\\\sqrt {13} = \sqrt {13}[/tex]
It is fulfilled!
Triangle 2:
[tex]25 = \sqrt {2 ^ 2 + (3 \sqrt {2}) ^ 2}\\25 = \sqrt {4+ (9 * 2)}\\25 = \sqrt {22}[/tex]
It is not fulfilled!
Triangle 3:
[tex]43 = \sqrt {2 ^ 2 + (3 \sqrt {3}) ^ 2}\\43 = \sqrt {4+ (9 * 3)}\\43 = \sqrt {4+ (9 * 3)}\\43 = \sqrt {31}[/tex]
It is not fulfilled!
ANswer:
Triangle A
