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SHASHI KANT

· started a discussion

· 1 Months ago

solution doubt (Question:1096397.0)

how can we assume the value of OQ=X/2 in semicircle

Question:

Find the ratio of areas of inscribed square in a semicircle and a circle while the radii of circle and semicircle are equal ?


Options:
A)

 2 : 5

B)

 3 : 5

C)

 1 : 2

D)

 1 : 3

Solution:

 Let 'r' be the radius of the semicircle

and 'x' be the side of the inscribed square.

  

In  ∆   OQR,

r2 = x2 + x22   

r2 =  54x2→x2=45r2   

∴    Area of the square =  45r2 sq.unit   

Again, let 'y' be side of the square

inscribed in the circle of same

radius.

  

Area of square=y2

= 2r22   sq. unit = 2r² sq. unit

Required ratio = 4r25   : 2r2

= 2r2 25:1=     2r2[2 : 5] = 2 : 5

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