If side \( A \) is 3 cm , and side \( B \) is 4 cm , what value must side \( C \) be in order for \( A B C \) to be a right triangle? 8 cm 9 cm 5 cm 6 cm

To determine the length of side \( C \) for triangle \( ABC \) to be a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, \( A^2 + B^2 = C^2 \). So, with sides \( A = 3 \) cm and \( B = 4 \) cm, we calculate \( 3^2 + 4^2 = C^2 \); that's \( 9 + 16 = C^2 \). Therefore, \( C^2 = 25 \) cm, leading us to \( C = 5 \) cm. So, the value of side \( C \) must be 5 cm. You might often have to determine if a triangle is right-angled using alternative side combinations; don’t forget the other angle properties and side combinations! Just remember, the largest side, \( C \), in a right triangle is always opposite the right angle—this makes checking your triangle's sides easy, fun, and a little bit of a puzzle.