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In the figure \(ABCD\) is a rectangle. \(DX = AX/2\). Point \(A'\) is the reflection of point \(A\) on \(BX\). Then find the ratio of the area of red region to the area of blue region. Give your answer to correct two decimal places.

 

 Jan 12, 2021
 #1
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Area of rectangle = (AX + DX) (AB)  =  (AX + AX/2)(AB)   =   (3/2)AX * AB    (1)

 

AX = XA'

AB = BA'

 

The white area  =  area of two right triangles with legs AX and AB  =   2  ( 1/2) AX * AB =   AX * AB   (2)

 

The blue area = area of right triangle with legs  AX/2  and AB  = (1/2) AX/2 *  AB  = AX* AB / 4   (3)

 

The  red area  =    (1)  - [ (2) +  (3)  ]  =

 

(AX * AB)   [  3/2  -  ( 1 + 1/4 )  ]  =    (AX * AB ) [ 3/2 - 5/4]   =  (AX * AB)  [  1/4 ] =  AX*AB / 4

 

Red Area = Blue Area....so their  ratio   1  / 1   =  1

 

 

cool cool cool

 Jan 12, 2021

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