OG详解-OG10 数学1 Q21

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 two legs. 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 = √1,​017 . 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.