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 apply the Pythagorean theorem, which states that for a triangle with sides a, b, and c (where c is the longest side), the equation \(a^2 + b^2 = c^2\) must hold true.

The sides of triangle DEF are 50, 40, and 32. First, we identify the longest side, which is 50. We will consider 50 as side c, and 40 and 32 as sides a and b.

Now we calculate:

1. \(a^2 + b^2 = 40^2 + 32^2 = 1600 + 1024 = 2624\)
2. \(c^2 = 50^2 = 2500\)

Now we compare \(a^2 + b^2\) with \(c^2\):

\[
2624 \neq 2500
\]

Since the Pythagorean theorem does not hold, triangle DEF is not a right triangle.

Therefore, the answer is **0**.