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Geometry and Trigonometry Difficulty: Easy

A right triangle has legs with lengths of $11$ centimeters and $9$ 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 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’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 $c squared equals 202$ . Taking the square root of each side of this equation yields $c = \pm \sqrt{202}$ . Since $c$ represents a length, $c$ must be positive. Therefore, the length of the triangle’s hypotenuse, in centimeters, is $StartRoot 202 EndRoot$ .

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 $c^{2} = 11^{2} + 9^{2}$ .