Find the probability that a point chosen at random inside the large triangle is in the small triangle.
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find the area of both triangles
it might be useful to know that any linear scale translates into a squared scale when it comes to area
for example: a 2x2 square has linear sides of 2, and an area of 4
if we scale it by 3; the sides become 3(2), and the area is therefore 3(2)*3(2),
or just 3^2 (4)
15k = 4, when k=4/15, so our linear scale is 4/15 to work with in this case
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lets spose we wanted to work the ratio of the example on squares ...
6k = 2, when k=2/6 = 1/3
k^2 = 1/9
now the areas of our square example is 36 and 4: 4/36 = 1/9 .... so what can we conject from this?
lets see if the shape matters
the area of the larger is 15h/2 for whatever the height is
the area of the smaller is 15(4/15) * h(4/15)/2
doesnt seem to matter what shape it is, as long as they are similar shapes :)