A right triangle has legs with lengths of 11 centimeters and 9 centimeters. What is the length of this triangle's

Question

A right triangle has legs with lengths of 11 centimeters and 9 centimeters. What is the length of this triangle's hypotenuse, in centimeters?

Accepted Answer

Choice B is correct. The Pythagorean theorem states that for a right triangle, c 2 = a 2 + b 2 , where c represents the length of the hypotenuse and a and b represent the lengths of the legs. It&rsquo;s given that a right triangle has legs with lengths of 11 centimeters and 9 centimeters. Substituting 11 for a and 9 for b in the formula c 2 = a 2 + b 2 yields c 2 = 11 2 + 9 2 , which is equivalent to c 2 = 121 + 81 , or c 2 = 202 . Taking the square root of each side of this equation yields c = &#177; 202 . Since c represents a length, c must be positive. Therefore, the length of the triangle&rsquo;s hypotenuse, in centimeters, is 202 . Choice A is incorrect. This is the result of solving the equation c 2 = 11 2 + 9 2 , not c 2 = 11 2 + 9 2 . Choice C is incorrect. This is the result of solving the equation c 2 = 11 2 + 9 2 , not c 2 = 11 2 + 9 2 . Choice D is incorrect. This is the result of solving the equation c = 11 2 + 9 2 , not c 2 = 11 2 + 9 2 .

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