Euclid1

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

Correct answer:

c₁ =  26.66 cm
c₂ =  0.34 cm

Step-by-step explanation:

$$\begin{gathered} c_1+c_2=27 \\ {c}_1\cdot c_2=3^2 \\ {x}^2-27x+9=0 \\ a=1;b=-27;c=9 \\ D=b^2-4ac=27^2-4\cdot 1\cdot 9=693 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{27\pm \sqrt{693}}{2}}={\displaystyle \frac{27\pm 3\sqrt{77}}{2}} \\ {x}_{1,2}=13.5\pm 13.1624465811 \\ {x}_1=26.6624465811 \\ {x}_2=0.337553418912 \\ \text{ Factored form of the equation: } \\ (x-26.6624465811)(x-0.337553418912)=0 \\ {c}_1=26.66\text{ cm} \end{gathered}$$

$c_2=0.34\text{ cm}$

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