Question

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?

Answer 1

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