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.
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