SOLUTION: Grace is 4 ft. tall and standing in the light of a 20 ft. tall lamppost. her shadow is 8 ft. long. If she moves 1 ft. closer to the lamppost, by how much will her shadow decrease?

Algebra ->  Length-and-distance -> SOLUTION: Grace is 4 ft. tall and standing in the light of a 20 ft. tall lamppost. her shadow is 8 ft. long. If she moves 1 ft. closer to the lamppost, by how much will her shadow decrease?      Log On


   

Question 561513: Grace is 4 ft. tall and standing in the light of a 20 ft. tall lamppost. her shadow is 8 ft. long. If she moves 1 ft. closer to the lamppost, by how much will her shadow decrease?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
using similar triangles ___ 4 / 8 = 20 / (d + 8)

"cross" multiplying ___ 4d + 32 = 160 ___ d = 32 ___ this is the starting distance from the lamppost

4 / s = 20 / (31 + s) ___ 4s + 124 = 20s ___ 31 / 4 = s

her shadow decreases 1/4 ft or 3 in