Question

A9 A rectangle and a semicircle are drawn as follows so that AB = 4 and AC = 1. Find BD.

Answer 1

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

                $=\pi*r^2\\\\=\pi \times [\frac{x+2}{2}]^2\\\\=\frac{\pi}{4}\times (x+2)^2$  Square Unit

                              ---------------------------------(2)

Equating (1) and (2)  

  $\rightarrow 4 \times (x+2)=\frac{\pi}{4}\times (x+2)^2\\\\ \text{Cancelling (x+2) from both sides}\\\\ \rightarrow x+2=0\\\\\rightarrow x\neq -2,\text{Segment Length can't be negative}\\\\\rightarrow 4=\frac{\pi}{4}\times (x+2)\\\\\rightarrow x=\frac{16}{\pi}-2\\\\\rightarrow BD=\frac{16}{\pi}-2+2\\\\\rightarrow BD=\frac{16}{\pi}$

  $BD=\frac{16\times 7}{22}\\\\BD=5.090909.......\\\\BD=5.1 \text{Unit}$        

Answer 2

Answer:

BD would be 17 , hope this helps !!