Davion's gas tank can hold 22.6 gallons of gasoline. Currently, Davion's gas tank is one-third full. His car's gas mileage is 31 miles per gallon. Which expression can be
used to find the number of miles Davion can drive on one-third of a gas tank?

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