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

Explanation

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 .