Jessica's Furniture Store buys a couch at a wholesale price of \$113.00$113.00dollar sign, 113, point, 00.
If the markup rate at Jessica's Furniture Store is 45\%45%45, percent, what is the markup for the couch?
\$\$ dollar sign, space

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

a

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