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[ermines]

Help... (illusion)

could someone figure out the answer...

 

[ermines]

...excuse me, but why can't i see the .gif i attached...

 

[damgo]

Are either of those shapes actually triangles? Look carefully at the intersection of the diagonal with the grid. Or calculate the slopes of the diagonal lines.

 

[Pauly Man]

I think Damgo is right.

If you calculate the area of the whole "triangle" you get:

Area = (1/2)*(13*5) = 32.5

However if you calculate the area of each individual piece you get:

Red: = (1/2)*(8*3) = 12
Light Green: = 8
Dark Green: = (1/2)*(5*2) = 5
Yellow: = 7

Adding these values up we get a total area of 32.

There is a contradiction here, therefore there is something fishy going on, and I think it has to do with the assumption that the apparent triangles are truly triangles.

 

[Ben-CS]

The four shapes do not come together to make a triangle. The small triangle (dark green) is a right triangle with legs 2 and 5; the large triangle (red) is a right triangle with legs 3 and 8. They are not congruent.

P.S.: You cannot see the attached image because it is an attachment. Veiw the attachment by selecting the link. If you want to insert an image, you will have to use IMG tags. https://www.physicsforums.com/misc.php?action=bbcode#imgcode

 

[ermines]

so my answer was right, yehey...