Carpet

The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diagonal.

Correct answer:

x =  10.18034 m

Step-by-step explanation:

$$\begin{gathered} a+b=10 \\ c+d=5 \\ {x}^2=b^2+c^2 \\ {1}^2=a^2+d^2 \\ y=x^2=(10-a{)}^2+(5-\sqrt{1-a^2}{)}^2 \\ y=x^2=-10\sqrt{1-a^2}-20a+126 \\ {y}^{\mathrm{\prime }}={\displaystyle \frac{10a}{\sqrt{(}1-a^2)}}-20 \\ {y}^{\mathrm{\prime }}=0 \\ a={\displaystyle \frac{2}{\sqrt{5}}}=0.894427191m \\ x=\sqrt{y}=\sqrt{-10\sqrt{(}1-a^2)-20a+126} \\ x=10.18034\text{ m} \end{gathered}$$

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