For the right triangle shown, a = 4 and b = 5. Which expression represents the value of c?

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Accepted Answer

Choice D is correct. By the Pythagorean theorem, if a right triangle has a hypotenuse with length c and legs with lengths a and b, then c 2 = a 2 + b 2 . In the right triangle shown, the hypotenuse has length c and the legs have lengths a and b. It’s given that a = 4 and b = 5. Substituting 4 for a and 5 for b in the Pythagorean theorem yields c 2 = 4 2 + 5 2 . Taking the square root of both sides of this equation yields c = ±√ 4 2 + 5 2 . Since the length of a side of a triangle must be positive, the value of c is √ 4 2 + 5 2 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

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