Letter fabric length

The letter H is part of a square surrounded by a circle with a diameter of 42 cm. Is a fabric 1 meter long enough to make this letter? Neglect the thickness of the fabric.

Final Answer:

x =  0.891 m

Step-by-step explanation:

$$\begin{gathered} D=42\text{cm} \\ r=D/2=42/2=21\text{cm} \\ a=D/\sqrt{2}=42/\sqrt{2}=21\sqrt{2}\text{cm}\doteq 29.6985\text{cm} \\ {x}_0=a+a+a=29.6985+29.6985+29.6985=63\sqrt{2}\text{cm}\doteq 89.0955\text{cm} \\ x=x_0\to \text{m}=x_0:100\text{m}=89.0955:100\text{m}=0.89095\text{m} \\ x<1\text{m} \end{gathered}$$

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