For the right triangle shown, a = 4 and b = 5. Which expression represents the value of c ?
Correct answer: D. √42 + 52
- A. 4 + 5
- B. √(4)(5)
- C. √4 + 5
- D. √42 + 52
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 .
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