The side lengths are labeled as follows:

a

b

c

The angle opposite the side labeled c is a right angle.

A note indies the figure is not drawn to scale.

Question

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

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 = /mo> 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.

Question the-si