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.

Guest Oct 16, 2020

#2**+2 **

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(6^{2} + 10^{2})

x = 3.56997

Dragan Oct 17, 2020