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Geometry and Trigonometry Difficulty: Medium

A right triangle has legs with lengths of $28$ centimeters and $20$ centimeters. What is the length of this triangle's hypotenuse, in centimeters?

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Explanation

Choice B is correct. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. It's given that the right triangle has legs with lengths of $28$ centimeters and $20$ centimeters. Let $c$ represent the length of this triangle's hypotenuse, in centimeters. Therefore, by the Pythagorean theorem, $28^{2} + 20^{2} = c^{2}$ , or $1,184 equals c squared$ . Taking the positive square root of both sides of this equation yields $StartRoot 1,184 EndRoot equals c$ , or $4 StartRoot 74 EndRoot equals c$ . Therefore, the length of this triangle's hypotenuse, in centimeters, is $4 StartRoot 74 EndRoot$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the square of the length of the triangle’s hypotenuse.