It is given that, AC=1 Unit
CM=x Unit, MN=1 Unit
BD=x+1+1=x+2 Unit
AB=4 Unit
Area of Rectangle =Length * Breadth
=4 * (x+2) Square Unit ---------------------(1)
Area of Circle having (Diameter =x+2 Unit) will be equal to
[tex]=\pi*r^2\\\\=\pi \times [\frac{x+2}{2}]^2\\\\=\frac{\pi}{4}\times (x+2)^2[/tex] Square Unit
---------------------------------(2)
Equating (1) and (2)
[tex]\rightarrow 4 \times (x+2)=\frac{\pi}{4}\times (x+2)^2\\\\ \text{Cancelling (x+2) from both sides}\\\\ \rightarrow x+2=0\\\\\rightarrow x\neq -2,\text{Segment Length can't be negative}\\\\\rightarrow 4=\frac{\pi}{4}\times (x+2)\\\\\rightarrow x=\frac{16}{\pi}-2\\\\\rightarrow BD=\frac{16}{\pi}-2+2\\\\\rightarrow BD=\frac{16}{\pi}[/tex]
[tex]BD=\frac{16\times 7}{22}\\\\BD=5.090909.......\\\\BD=5.1 \text{Unit}[/tex]
