Lauren pays $19.99 for a membership fee to an online music store. lauren buys songs from a new album at the price of $0.99 each. she paid a total of $21.97 for the membership fee and the songs. which represents the number of songs lauren bought? show work!
(a) 1 songs
(b) 2 songs
(c) 3 songs
(d) 4 songs

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