Problem: The length of rectangle ABCD is 5 inches and its width is 3 inches. Diagonal AC is divided into three equal segments by points E and F. The area of triangle BEF, expressed in square inches, is:
Answer Choices:
A. 23​
B. 35​
C. 25​
D. 31​34​
E. 31​68​
Solution:
The area of triangle ABC equals 21​⋅5⋅3=215​. Since AE=EF=FC, the area of triangle BEF equals 31​ of the area of triangle ABC, that is, 31​⋅215​=25​.