Carpet

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

Correct answer:

x =  10.18034 m

Step-by-step explanation:

$$\begin{gathered} a+b=10 \\ c+d=5 \\ {x}^2=b^2+c^2 \\ {1}^2=a^2+d^2 \\ y=x^2=(10-a{)}^2+(5-\sqrt{1-a^2}{)}^2 \\ y=x^2=-10\sqrt{1-a^2}-20a+126 \\ {y}^{\prime }=\frac{10a}{\sqrt{(}1-a^2)}-20 \\ {y}^{\prime }=0 \\ a=\frac{2}{\sqrt{5}}=0.89442719099992m \\ x=\sqrt{y}=\sqrt{-10\sqrt{(}1-a^2)-20a+126} \\ x=10.18034\text{m} \end{gathered}$$

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