OG详解-OG8 数学2 Q5

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 c² = a² +b². 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 c² = 4² +5². Taking the square root of both sides of this equation yields c = ± √4²​+5² . Since the length of a side of a triangle must be positive, the value of c is √4²​+5².
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.