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February 18, 2018, 10:54:27 AM
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: What is the difference between the 2 triangles?  ( 4553 )
« : August 17, 2007, 08:44:55 PM From Shrinidhi»

What is the difference between the 2 triangles?

Check out the attached pic. It is a very common puzzle, but an interesting one.
Can you tell how the hole in the second triangle??

PS: Click on the image to enlarge it.

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« #1 : August 18, 2007, 10:08:53 PM From spazinvader»

I don't understand your question properly.
Could you tell me the question in another way?
« #2 : August 18, 2007, 10:51:28 PM From Shrinidhi»

The top and the bottom triangles are same (in terms of height and base width). Also the number of squares in each color are same. However, if you just rearrange those colored squares, you get a space for an extra square (see the hole). How is this possible?
« #3 : September 13, 2007, 10:38:36 AM From vishwakarma.deepak»

Dear srinidhi, i don't know how famous this question is...but question is fake...

if u calculate area of a 13unit by 5 unit triangle, it'll come 65/2=32.5 sq units

calculating area of every element and adding them, here in your problems the area of first image is 8+7+1/2(5x2)+1/2(8x3) =  32 sq units and
that of the second one is
     1/2(5x3)+7+8+1/2(8x3) +1 = 33 sq units

So, in first fig area is shown .5 sq unit less in second image it's shown .5 sq unit more...hence a difference to tatal 1 sq unit...

if u observe both the images on vertical axis lines, u'll clearly see the difference...first image is a faked to a bit less in area...hypotenuse is concave...and on the other hand the second figure is faked to be .5 sq unit bigger by convexing hypotenuse...

Pls correct me if Im worng...

« #4 : September 20, 2007, 09:35:15 AM From dm07b006»

dear srindhi,,,,,,,,,,,,,,,
              it the concept of areas through  integration
whatever we calculate by using lrngth , breadth .......... are not exact
i think viswakarma is almost correct ,,,,,,,,,,,,,,
« #5 : September 26, 2007, 05:01:20 PM From vishwakarma.deepak»


Dear could u pls specify ur statement...

it the concept of areas through  integration
whatever we calculate by using lrngth , breadth ..........

here we do not have exact equations of sides of triangles. if u try to calculate equations using coordinates, integrated area would be same for both the trianges. as coordinates of side edges are same in both triangles.

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