In AB, DE and GF are parallel to each other and AD, BG and EF ar parallel to each other . If CD: CE = CG:CB = 2:1 then the value of area `(triangleAEG): area (triangleABD) ` is equal to (a) 7/2 (b)3 (c)4 (d)9/2

Options

A. `7//2`
B. 3
C. 4
D. `9//2`

Answer

b

Explanation

Let A be the origin, `vec(AB) = veca , vec(AD) = vecb`
so, `vec(AE) , vecb + 3/2 veca, vec(AG) = veca + 3vecb`
`(1/2|(veca+3vecb)xx(vecb+3/2veca)|)/(1/2|vecaxxvecb|)`