To determine whether 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) must equal the sum of the squares of the lengths of the other two sides.
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Assign the sides:
- Let's take 50 cm as the longest side (hypotenuse).
- The other sides are 40 cm and 32 cm.
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Apply the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] where \( c \) is the hypotenuse.
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Calculate:
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\( 40^2 + 32^2 \): \[ 40^2 = 1600 \] \[ 32^2 = 1024 \] \[ 40^2 + 32^2 = 1600 + 1024 = 2624 \]
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\( 50^2 \): \[ 50^2 = 2500 \]
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Compare: \[ 40^2 + 32^2 = 2624 \quad \text{and} \quad 50^2 = 2500 \]
Since \( 2624 \neq 2500 \), triangle DEF is not a right triangle.
Therefore, the answer is False.
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