To determine if triangle DEF with sides measuring 50 cm, 40 cm, and 32 cm is a right triangle, we can use the Pythagorean theorem. According to this theorem, for a triangle to be a right triangle, the square of the length of the longest side (hypotenuse) should equal the sum of the squares of the other two sides.
Let's denote the sides:
- \( c = 50 \) cm (the longest side)
- \( a = 40 \) cm
- \( b = 32 \) cm
Now, we apply the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
Calculating each term:
- \( c^2 = 50^2 = 2500 \)
- \( a^2 = 40^2 = 1600 \)
- \( b^2 = 32^2 = 1024 \)
Now, adding \( a^2 \) and \( b^2 \): \[ a^2 + b^2 = 1600 + 1024 = 2624 \]
Now we compare: \[ c^2 (2500) \neq a^2 + b^2 (2624) \]
Since \( 2500 \) does not equal \( 2624 \), triangle DEF is not a right triangle.
Therefore, the answer is False.
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