Final answer:
Triangle C, with side lengths 3, 4, and 5, can be proven to be a right triangle.
The correct answer is C.
Step-by-step explanation:
The given side lengths of a triangle are:
A) 5, 10, 12
B) 6, 5, 3
C) 3, 4, 5
D) 6, 8, 10
To determine if a triangle is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Using the Pythagorean theorem, we can check the given side lengths:
A) 5² + 10² = 25 + 100 = 125 ≠ 12²
B) 6² + 5² = 36 + 25 = 61 ≠ 3²
C) 3² + 4² = 9 + 16 = 25 = 5²
Therefore, based on the given side lengths, triangle C, with side lengths 3, 4, and 5, can be proven to be a right triangle.