To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem, which states that 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 lengths of the other two sides.
Let's identify the sides:
- a = 32 cm
- b = 40 cm
- c = 50 cm (hypotenuse, since it is the longest side)
Now we check if \( c^2 = a^2 + b^2 \):
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Calculate \( c^2 \): \[ c^2 = 50^2 = 2500 \]
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Calculate \( a^2 + b^2 \): \[ a^2 + b^2 = 32^2 + 40^2 = 1024 + 1600 = 2624 \]
Now we compare:
- \( c^2 = 2500 \)
- \( a^2 + b^2 = 2624 \)
Since \( c^2 \) (2500) does not equal \( a^2 + b^2 \) (2624), triangle DEF is not a right triangle.
The answer is False.