Twenty-one students at a school have an allergy to peanuts, shellfish, or both.
 fourteen students at the school are allergic to peanuts.
 twelve students at the school are allergic to shellfish.
how many of the students are allergic to both peanuts and shellfish?
a 12
b 7
c 5
d 2

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