Euclid1

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

Result

c1 =  26.66 cm
c2 =  0.34 cm

Solution:

c1+c2=27 c1⋅c2=32   x2−27x+9=0  a=1;b=−27;c=9 D=b2−4ac=272−4⋅1⋅9=693 D>0  x1,2=−b±D2a=27±6932=27±3772 x1,2=13.5±13.162446581088 x1=26.662446581088 x2=0.33755341891182   Factored form of the equation:  (x−26.662446581088)(x−0.33755341891182)=0 c1=26.66  cm 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 13.162446581088 \ \\ x_{1} = 26.662446581088 \ \\ x_{2} = 0.33755341891182 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -26.662446581088) (x -0.33755341891182) = 0 \ \\ c_1 = 26.66 \ \text{ cm }
c2=0.34  cm c_2 = 0.34 \ \text{ cm }

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