# Euclid1

Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?

Correct result:

c1 =  26.66 cm
c2 =  0.34 cm

#### Solution:

$c_1+c_2 = 27 \ \\ c_1 \cdot c_2 = 3^2 \ \\ \ \\ \ \\ x^2 -27x +9 =0 \ \\ \ \\ a=1; b=-27; c=9 \ \\ D = b^2 - 4ac = 27^2 - 4\cdot 1 \cdot 9 = 693 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 27 \pm \sqrt{ 693 } }{ 2 } = \dfrac{ 27 \pm 3 \sqrt{ 77 } }{ 2 } \ \\ x_{1,2} = 13.5 \pm 13.1624465811 \ \\ x_{1} = 26.6624465811 \ \\ x_{2} = 0.337553418912 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -26.6624465811) (x -0.337553418912) = 0 \ \\ \ \\ c_1 = 26.66 \ \text{cm}$

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