In the figure, the area of rectangle abcd is 100 square inches. arranged as shown, points e and f are selected on bd, so that 2(be + fd) = 3ef. what is the area of triangle cef?

The area of CEF will be calculated as follows:
The ratio of (BE+FD):EF is:
3:2
But the area of BDC=1/2ABCD
thus
BDC=1/2*100=50 in
hence the area of CEF will be:
(fraction of CEF)×(Area of BDC)
fraction of CEF=2/5
hence the area will be:
2/5×50
=20 in²