Elizabeth brought a box of donuts to share. there are two-dozen (24) donuts in the box, all identical in size, shape, and color. six are jelly-filled, 7 are lemon-filled, and 11 are custard-filled. you randomly select one donut, eat it, and select another donut. find the probability of selecting two lemon-filled donuts in a row.

geometry: triangles

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lessons

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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+

25.45584