Question

If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.

Answer 1

To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the longest side of triangle DEF is 50. So, if triangle DEF is a right triangle, the equation should hold true:

50^2 = 40^2 + 32^2

2500 = 1600 + 1024

2500 ≠ 2624

Since the equation does not hold and the sum of the squares of the two shorter sides is not equal to the square of the longest side, we can conclude that triangle DEF is not a right triangle.

Therefore, the answer is 0.