A florist has 56 roses and 70 carnations to make table centerpieces. He wants to put an equal number of roses and carnations into each centerpiece. Use the drop-down menus to complete the statements below about the number of centerpieces the florist can make if he uses all the flowers.

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