What percent of pure gold is in a watchcase that is 16 carats fine? in a chain that is 12 carats fine? in a ring that is 14 carats fine?

In 16 carats : 66.67%

In 12 carats : 50%

In 14 carats : 58 1/3%

Step-by-step explanation:

geometry: triangles

solvers

lessons

answers archive

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