To determine if triangle ABC with sides measuring 50, 42, and 35 is a right triangle, we can use the Pythagorean theorem which states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the longest side.
Here, the longest side is 50. We have:
\[ a = 42, , b = 35, , c = 50 \]
Now let's check if:
\[ 42^2 + 35^2 = 50^2 \]
Calculating each side:
\[ 42^2 = 1764 \] \[ 35^2 = 1225 \] \[ 50^2 = 2500 \]
Now summing \( a^2 \) and \( b^2 \):
\[ 1764 + 1225 = 2989 \]
This does not equal \( 2500 \):
\[ 2989 \neq 2500 \]
Since \( a^2 + b^2 \neq c^2 \), triangle ABC is not a right triangle.
Thus, the answer is:
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