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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.(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 in a right triangle with legs \( a \) and \( b \) and hypotenuse \( c \), the following equation holds:

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

Here, we need to identify the longest side, which will be considered as the hypotenuse. In this case, the longest side is 50.

Thus, we will check if:

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

Calculating the squares:

- \( 40^2 = 1600 \)
- \( 32^2 = 1024 \)
- \( 50^2 = 2500 \)

Now, adding the squares of the two shorter sides:

\[ 1600 + 1024 = 2624 \]

Now comparing:

\[ 2624 \neq 2500 \]

Since \( 40^2 + 32^2 \) does not equal \( 50^2 \), triangle DEF is not a right triangle.

Therefore, the answer is **0**.