sud21 wrote:The sides of a triangle is a, b, and c. Is it a right triangle?
1). a^2+b^2=3^2+4^2
2). a^2+c^2=3^2+5^2
We have not been given that a, b, c are integers, so let's be very careful here, they could probably trick us with the well known Pythagorean triplet 3-4-5 to assume anything pleasing from our own end.
(1) Since a^2 + b^2 = 3^2 + 4^2 is true even when a is √19 and b is √6 or vise-versa, hence a and b are not necessarily 3 and 4. Even if a and b are 3 and 4, we don't know what angle they include. Hence, this statement is not sufficient.
(2) Since a^2 + c^2 = 3^2 + 5^2 is true even when a is √19 and c is √15 or vise-versa, hence a and c are not necessarily 3 and 5. Even if a and b are 3 and 5, we don't know what angle they include. Hence, this statement is not sufficient.
Taking the two statements together, with a^2 + b^2 = 25 and a^2 + c^2 = 34, we cannot find the value of c^2 uniquely, which could have helped us to decide on whether a^2 + b^2 = c^2 or not. Things are still not sufficient, [spoiler]hence E[/spoiler].
