Question

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

Answer 1

BD would be 17 , hope this helps !!

Answer 2

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 * [(x+2)/(2)]^2\\\\=(\pi)/(4)* (x+2)^2` Square Unit

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

Equating (1) and (2)

`\rightarrow 4 * (x+2)=(\pi)/(4)* (x+2)^2\\\\ \text{Cancelling (x+2) from both sides}\\\\ \rightarrow x+2=0\\\\\rightarrow x\\eq -2,\text{Segment Length can't be negative}\\\\\rightarrow 4=(\pi)/(4)* (x+2)\\\\\rightarrow x=(16)/(\pi)-2\\\\\rightarrow BD=(16)/(\pi)-2+2\\\\\rightarrow BD=(16)/(\pi)`

`BD=(16* 7)/(22)\\\\BD=5.090909.......\\\\BD=5.1 \text{Unit}`