Use the Converse of the Pythagorean Theorem to determine whether a right triangle can be formed given sides a , b , and c , where a=6 , b=10 , and c=12 .
The Converse of the Pythagorean Theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
In this case, we have a=6, b=10, and c=12.
According to the converse of the Pythagorean Theorem, if a^2 + b^2 = c^2, then the triangle is a right triangle.
Substituting the given values, we have:
6^2 + 10^2 = 12^2
36 + 100 = 144
136 = 144
Since 136 ≠ 144, it means that a right triangle cannot be formed with sides of length 6, 10, and 12.