Buses from two different bus routes each stop at the same corner at 9 A. M. Buses from one route stop at that corner every 9 minutes. Buses from the other route stop there every 12 minutes. What is the fewest number of minutes that will pass until the next time buses from both routes are at that corner at the same time? a
21 minutes
b
36 minutes
c
54 minutes
d
108 minutes

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 distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula

okay..i will pick 8!