OG详解-OG2 数学2 Q27

The correct answer is 113. It’s given that the legs of a right triangle have lengths  24 centimeters and 21 centimeters. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the twolegs.    It follows that if h  represents the length, in centimeters, of the hypotenuse of the right triangle, h²  = 242  +212. This equation is equivalent to  h²  = 1,017. Taking the square root of each side of this equation yields  h =  √1017​. This equation can be rewritten as  h = ·√9•113​ , or  h = √9​• √113​. This equation is equivalent to h = 3 √113​. It’s given that the length of the triangle’s hypotenuse, in centimeters, can be written in the form  3 √d​ . It follows that the value of d  is  113.