Can you solve this Mystry?

Muslimz

Allahisenough4me
Try solving this ( hope puzzles are allowed in this section)
i21u1z.gif
 

arzafar

Junior Member
easy really!

i21u1z-solved.GIF


The space saved up from the 4 dotted areas (and others) forms the empty square in the second pic
 

revert2007

Love Fishing
The key is that the two triangles
aren't similar
the reason a blank white square appears in the bottom
diagram is that in the top diagram, the green right triangle at the
top and the red right triangle at the bottom are not similar
triangles. As a result, the area of the entire figure does not remain
the same when you move the two triangles.

This refers to the top diagram: The acute
angle at the bottom left of the top green triangle is

tan(beta) = 2/5,

and the acute angle at the bottom left of the larger red
triangle at the bottom is

tan(alpha) = 3/8.

Put another way, the two smaller sides of the smaller green triangle
are 2:5, but the ratio of the sides of the larger red one is 3:8.
Clearly, 2:5 =/= 3:8, and the red and green triangles are not similar.

Why should this matter? Because if the red and green right triangles
were similar, you could place the green one at the bottom left and the
red one at the top right, and leave no blank white square when you
moved the orange figure. But the triangles are not similar, so when
you place the green one in the lower position and the red one in the
higher position, you decrease the total area of the larger triangle
that contains the red and green triangle and the other orange figure.

for the two triangles to actually
act as you see on that site, the big triangle that contains both of
them (as well as the orange figure) would have to have a curved,
concave-shaped hypotenuse in one case and a curved, convex-shaped
hypotenuse in the other. :SMILY259::SMILY259::SMILY259::SMILY259:

source

p.s:am not too smart for hard work but am smart for SMART work lol
 

abu'muhammad

Junior Member
:salam2:

thnx for the puzzle. :)

Both triangles have same areas yet arrangements make different shapes.

In the first arrangement orange figure is over the green figure that makes figures balanced or even. The two slots of orange figure gets fitted in three slots of green figure. This makes 3 lines of 5 squares in vertical manner , in all 15 squares .

In the second arrangement orange figure is on the side of green figure making 2 lines of 8 squares in horizontal manner, making space of 16 squares, but there are in all 15 squares no matter how squares of orange and green figures counted. This extra space of 1 square leave a gap in second arrangement.

This is due to different geometrical arrangements, As in figure 1 the other coloured figures touch red figure from the side of ‘height of red figure’. In figure 2 the other coloured figures touch red figure from ‘side of base of red figure’. This changes the arrangement of constituent figures giving variety in shape. Still the figures could be arranged into further different arrangements although the areas of triangles remaining same in all arrangements. so net no loss no gain in areas of figures but a change in geometrical shape.

:salam2:
 
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