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.(1 point).

Answer 1

To determine if triangle DEF with sides measuring 50, 40, and 32 is a right triangle, we can use the Pythagorean theorem. The theorem states that for a triangle with sides of lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the triangle is a right triangle if:

\[ a^2 + b^2 = c^2 \]

In this case, the longest side is 50. Hence, we identify \(a = 40\), \(b = 32\), and \(c = 50\). Now we check:

\[ 40^2 + 32^2 = 50^2 \]

Calculating each side:

\[ 40^2 = 1600 \] \[ 32^2 = 1024 \] \[ 50^2 = 2500 \]

Now adding \(40^2\) and \(32^2\):

\[ 1600 + 1024 = 2624 \]

Comparing \(2624\) with \(2500\):

Since \(2624 \neq 2500\), triangle DEF is not a right triangle.

Thus, the answer is:

\[ 0 \]