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Triangle inside a rectangle

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by anju » Thu Aug 14, 2008 11:20 am
ratio is 1
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by iplraf » Thu Aug 14, 2008 11:32 am
You're right!
Just need a little insight! :)
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by iplraf » Thu Aug 14, 2008 11:33 am
Could you explain why is that?
Last edited by iplraf on Thu Aug 14, 2008 2:51 pm, edited 1 time in total.
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by anju » Thu Aug 14, 2008 11:45 am
Area of a rect = l * b
Area of white triangls = 1/2 base * ht
if u notice base = l and ht = b
say l = 4 and b = 2
area of grey = area of rect - area of white triangle
= 8 - 4 = 4
Ratio = white/grey = 4/4 = 1
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by drizzle » Thu Aug 14, 2008 11:14 pm
"if a trinagle and a parallelogram lie on the same base and between the same parallel lines then area of tringale is half of area of parallelogram"

this is true of rectangle too
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by Ian Stewart » Fri Aug 15, 2008 7:52 am
There are a few ways to see that the ratio is 1:1, including a couple of good ways in the above posts. You could also do as follows:

-draw a vertical line from the top corner of the white triangle to the bottom of the rectangle. This divides the large rectangle into two smaller rectangles, and each is clearly half-white, half-shaded, since the edge of the white triangle is a diagonal of each smaller rectangle.
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