The Floral Place made this deposit: 72 twenties, 126 tens, 57 fives, 235 ones; 287 quarters, 312 dimes, 48 nickels, 347 pennies; and checks for $124.68, $132.08, $1.29, $5.79. They received no cash back. What is the total deposit?

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