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

A9 A rectangle and a semicircle are drawn as follows so that AB = 4 and AC = 1. Find-example-1
User Blow
by
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2 Answers

3 votes

Answer:

BD would be 17 , hope this helps !!

User Simone Porcu
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2 votes

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}

A9 A rectangle and a semicircle are drawn as follows so that AB = 4 and AC = 1. Find-example-1
User Alex Sorokoletov
by
8.6k points

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