A right triangle has legs with lengths of 24 centimeters and 21 centimeters. If the length of this triangle's hypotenuse,

Question

A right triangle has legs with lengths of 24 centimeters and 21 centimeters. If the length of this triangle's hypotenuse, in centimeters, can be written in the form 3 d , where d is an integer, what is the value of d ?

Accepted Answer

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, h 2 = 24 2 + 21 2 . This equation is equivalent to h 2 = 1,017 . Taking the square root of each side of this equation yields h = 1,017 . This equation can be rewritten as h = 9 /mo> 113 , or h = 9 /mo> 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 .

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