If triangle DEF

Question

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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 is a right triangle, we can use the Pythagorean theorem. For a triangle with sides \( a \), \( b \), and \( c \) (where \( c \) is the longest side), the triangle is a right triangle if:

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

Given the sides of the triangle are 50, 40, and 32, we first identify the longest side, which is 50. We can set \( a = 40 \), \( b = 32 \), and \( c = 50 \).

Now, calculate \( c^2 \) and \( a^2 + b^2 \):

\[ c^2 = 50^2 = 2500 \] \[ a^2 + b^2 = 40^2 + 32^2 = 1600 + 1024 = 2624 \]

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

Therefore, the answer is 0.