jmc

Question

In ABC, a point E is on AB with AE=1 and EB=2. Point D is on AC so that DE BC and point F is on BC so that EF AC. What is the ratio of the area of CDEF to the area of ABC? FIGURE

Accepted Answer

By similar triangles, we have [ADE] = 19[ABC]. Similarly, we see that [BEF] = 49[ABC]. Using this information, we get [ACFE] = 59[ABC]. Then, since [ADE] = 19[ABC], it follows that the [CDEF] = 49[ABC]. Thus, the answer would be 49. Sidenote: [ABC] denotes the area of triangle ABC. Similarly, [ABCD] denotes the area of figure ABCD.