Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right angle

Question

a:No, because 22 is not equal to 15
b:No, because 369 is not equal to 100
c:No, because 325 is not equal to 144
d:No, because 244 is not equal to 225

Answer 1

The correct answer is d: No, because 244 is not equal to 225. The Converse of the Pythagorean Theorem states that if the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is a right triangle. In this case, the sum of the squares of the shorter sides (10 and 12) is equal to 244, which is not equal to the square of the longest side (15 squared is 225). Therefore, the triangle is not a right angle.