Right triangle ABC has one leg of length 6 cm

 

Right triangle ABC has one leg of length 6 cm, one leg of length 12 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.     

 

c²  =  a² + b²     

 

hypotenuse²  =  6² + 12²     

hypotenuse  =  side of square     

 

side²  =  6² + 12²     

side²  =  36 + 144     

side²  =  180     

side¹  =  sqrt(180)     

side²  =  6 • sqrt(5)      The square root of 5 is an irrational number, and     

                                     therefore can't be expressed as a common fraction.     

_.