A 6 ounce drink costs $2.16 and a 10 ounce drink costs $3.25. Which drink is the better buy?

The ten ounce drink is a better deal.

The Explanation: Why? Well, since you are getting 10 ounces of a drink you spend only 32 cents on each ounce whereas with the 6 ounces you end up spending 36 cents per ounce. You might be spending more money on the ten ounces but when you break down the cost of the drink per ounce you figure out that it is the best deal possible!

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

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft