Of the red and green apples in a basket, 4/7 are red apples. of the green apples in the basket 2/9 are rotten. what fraction of the apples in the basket are rotten? if there are 63 apples altogether, how many green apples are rotten?

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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