This site introduces problems of Sansue, i.e. mathematics which Japanese schoolchildren learn at elementary school. Problems are selected mainly from entrance examinations of famous junior high schools for 6th grade Japanese schoolchildren (12 years old) to take. We found Sansue is not only one of subjects at school but one of Japanese culture. Please enjoy Japanese Sansue culture.
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Math New Drill (Level 1) : Geometry (Plane figure) △ ABC is divided into five triangles of equal area
△ ABC is divided into five triangles of equal area.
Find AD : DE : EC.
Answer
3:4:8
Solution
As △ABD ： △DBC ＝ 1 ： 4, AD : DE ＝ 1 : 4.
As △DFE ： △EFC ＝ 1 ： 2, DE : EC = 1 : 2.
DE ＝ 4 × 1/(1+2) ＝ 4/3
EC = 4/3 × 2 ＝ 8/3
Therefore, AD : DE : EC ＝ 1 ： 4/3 ： 8/3 ＝ 3 ： 4 ： 8.
