Triangle Puzzle....

sivarap · 18-10-2007, 11:35 AM

This is a forward I got in my mail.....the explanation is obvious but its the way we go about matters.........

We have learnt from our childhood that area of an entire body (triangle, circle, rectangle etc) is equal to the sum of area of the parts it contains... and even if these parts are arranged differently, the area remains unchanged... but this mail challenges this fact... Do let me know if you get an answer for this one...

Here's a puzzling new discovery:
Recently a professor in MIT has put a new theory on right-angled triangles that has challenged some accepted norms in Geometry. This theory, Prof. John Mentriffe says, will revolutionize area in mathematics that deals with calculation of motion objects in space and design of the Universe.
Any comments on the following?
I am not able to paste the picture so i am attaching it......

alsiladka · 18-10-2007, 12:30 PM

Both of them are 38 pieces of the grid (not complete, but in equal area).
The parts cannot be arrranged in such a way so as to leave gaps between them. The rule was that whatever way they are arranged, leaving no gaps, the area will be the same.

The_Devil_Himself · 18-10-2007, 12:33 PM

^^both are made up of 32.5 full grids I think[(13x5)/2=32.5].

Some lame trick I guess.

Vyasram · 18-10-2007, 08:47 PM

yeah, its a trick

in the second one the longest borders are shared, so this results in a small increase in size

could someone check it out without borders

also both of them are not triangles actually

first one is slighly concave and the second one is convex

solomon_paulraj · 19-10-2007, 10:17 AM

the answer is quite obvious.. watch the gap in the grid marked below.

alsiladka · 19-10-2007, 10:37 AM

Quote:

Originally Posted by solomon_paulraj

the answer is quite obvious.. watch the gap in the grid marked below.

Are you that dumb?
The greens in both the triangles are the same size and shape. The gaps you asked us to check, you go and check it in the first triangled. It is presend in both the triangles.

fun2sh · 21-10-2007, 10:47 AM

^^he is right

see the pic

in 1st figure the ACD is not a staight line. hence both 1st and 2nd figures are not a triangle n then u cant use the triangle property to calculate the area. u will hav to calculate the area by summin the areas of smaller figures whic gives 32 sq cm in both figures

i wonder how that mit professor didnt see that

note: one mistake in fig, for triangle CDF angle=tan inverse of (DF/CF) = 21.8 DIGREES