George and carmen went to a bicycle trip. they took a bus to their starting point, and then biked the rest. they traveled 300 kilometer in total, and they biked 70 kilometers more then they were bussed. let x = kilometers traveled by bike and y = kilometers traveled by bus find how many kilometers they traveled by bike.

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+

25.45584