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Right triangle ABC has one leg of length 6 cm, one leg of length 10 cm, and a right angle at A. A square has one side on the hypotenuse of triangle ABC and a vertex on each of the two legs of triangle ABC. What is the length of one side of the square in cm? Express your answer as a common fraction. 

 Oct 16, 2020
 #1
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The area is 65/8.

 
 Oct 17, 2020
 #2
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Right triangle ABC has one leg of length 6 cm, one leg of length 10 cm, and a right angle at A. A square has one side on the hypotenuse of triangle ABC and a vertex on each of the two legs of triangle ABC. What is the length of one side of the square in cm? Express your answer as a common fraction. 

 

Let the side of the square be  x

 

x / tan(B) + x + x / tan(C) = sqrt(62 + 102)

 

x = 3.56997  

 
 Oct 17, 2020

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