sat suite question viewer
A right triangle has legs with lengths of centimeters and centimeters. What is the length of this triangle's hypotenuse, in centimeters?
Explanation
Choice B is correct. The Pythagorean theorem states that for a right triangle, , where represents the length of the hypotenuse and and represent the lengths of the legs. It’s given that a right triangle has legs with lengths of centimeters and centimeters. Substituting for and for in the formula yields , which is equivalent to , or . Taking the square root of each side of this equation yields . Since represents a length, must be positive. Therefore, the length of the triangle’s hypotenuse, in centimeters, is .
Choice A is incorrect. This is the result of solving the equation , not .
Choice C is incorrect. This is the result of solving the equation , not .
Choice D is incorrect. This is the result of solving the equation , not .