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Geometry and Trigonometry / Right triangles and trigonometry Difficulty: Easy

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

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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 $c^{2} = a^{2} + b^{2}$ . In the right triangle shown, the hypotenuse has length $c$ and the legs have lengths $a$ and $b$ . It's given that $a equals 4$ and $b equals 5$ . 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 $c = \pm \sqrt{4^{2} + 5^{2}}$ . Since the length of a side of a triangle must be positive, the value of $c$ is $StartRoot 4 squared plus 5 squared EndRoot$ .

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.