A right triangle has legs with lengths of 24 centi meters and 21 centi meters. If the length of this triangle's hypotenuse, in centi meters, can be written in the form 3 d, where d is an integer, what is the value of d
Correct answer: A. 113
- A. 113
- B. 1
- C. 10
- D. 23
Explanation
.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, 2 2 2 h =24 +21 . This equation is equivalent to 2 h =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 centi meters,can be written in the form 3 d . It follows that the value of d is 113
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