Popular Missing Square Puzzle

How many number of times you have come across this image?

By now, you might have accepted the solution.

"The hypotenuse is bulged in bottom figure which accounts area equal to missing square!"

But is this really a solution to this puzzle? The issue illustrated in clear manner here!

And my opinion is here!

And how creator did manage to create that 'missing' square is illustrated here!

 

How Missing Square Puzzle Created?

That's how it was missed! 

Slope of diagonal must be 5/13 = 0.385

If we keep heights of red & green triangles constant as 3 & 2 respectively

then their bases should have been.

5/13 = 3/Base of red triangle 

Base of red triangle = 7.8

And,
 

Base of green triangle = 13 - 7.8 = 5.2

Creator of this optical illusion cleverly restricted 5.2 to 5 & extended 7.8 to 8.

Or we can say he altered heights of those triangles by keeping bases 8 & 5.

Now creator shuffles those colored blocks like shown below.

Missing square puzzle

Pink & Blue rectangles shuffled diagonally. Purple rectangle of size 15 

colored blocks is replaced by orange rectangle of size 16. Obviously orange

rectangle would have 1 white block & 15 colored blocks!

 

Missing square puzzle

   
                Area of colored region in top triangle = 0.5 x 13 x 5 = 32.5 Blocks

While in bottom triangle, 

Area of colored region + White Block = 0.5 x 13 x 5 =32.5 Blocks

Missing square puzzle

 Figured out here!  

How it is created? 

  

Source 

Origin of Missing Square Puzzle

First view this! 

Actually the diagonal drawn here isn't a true diagonal.....It's slope must be 5/13 = 0.385.

Two hypotenuses (of two triangles) have different slopes; red one having 3/8 = 0.375 &
green one has 2/5 = 0.4.

So both together can't form true diagonal of this rectangle neither hypotenuse of colored triangle.

So we need to calculate area of each colored shape differently & then add to get area of colored region.

Area of colored region = 12 + 5 + 15 = 32..... Not 32.5

So if it was halved by perfect diagonal then 32.5 - 32 = 0.5 of area would have been painted more.

This is half of that white space.This is also reason why non painted part of top rectangle covers area 12 + 5 + 16 = 33 i.e. 0.5 than expected 32.5 because of imperfect diagonal.

And if we calculate area of other part (non painted) of bottom rectangle as 12 +5 +15  = 32 ; again less by 0.5 if there was perfect diagonal.

Since it is not a perfect diagonal that white space is 'missing' 0.5 of colored area & 0.5 of white space is 'taken' from other part of rectangle.

That's why 1 white space there!