Apply the Pythagorean Theorem to decide whether a triangle with side length 16 mm, 30 mm, and 32 mm is a right triangle. explain with detail!
A: It is not a right triangle because 16^2 + 30^2 does not equal to 32^2.
B: It is no a right triangle because 16 + 30 does not equal to 32.
C: It is a right triangle because 16^2 + 30^2 = 1,156.
D: It is a right triangle because 16 + 30 = 46
The correct answer is option A: It is not a right triangle because 16^2 + 30^2 does not equal to 32^2.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, if the triangle with side lengths 16 mm, 30 mm, and 32 mm is a right triangle, then it should satisfy the Pythagorean Theorem.
To check, we can square the lengths of the sides and see if they produce the same values.
16^2 = 256
30^2 = 900
32^2 = 1024
The sum of the squares of the first two sides, 256 + 900, is not equal to the square of the third side, 1024. Therefore, the triangle does not satisfy the Pythagorean Theorem and is not a right triangle.