In triangle LMN, X is on LM and Y is on LN with XY parallel to MN, and $LX : XM = 3 : 4$. What is the ratio of the area of triangle LXY to the area of the quadrilateral XMNY?

Explanation

1. 01

   Triangle LXY is similar to triangle LMN with $LX : LM = 3 : 7$.

2. 02

   Area ratio = $3^2 : 7^2 = 9 : 49$.

3. 03

   The quadrilateral XMNY is what is left: $49 - 9 = 40$ parts.

4. 04

   So area of LXY : area of XMNY = $9 : 40$.