21. In triangle $P Q R$, the point $S$ is on $P Q$ so that the ratio of the length of $P S$ to the length of $S Q$ is $2: 3$. The point $T$ lies on $S R$ so that the area of triangle $P T R$ is 20 and the area of triangle SQT is 18 , as shown in the diagram.
What is the area of triangle $P Q R$ ?
A 100
B 90
C 80
D 70
E 60
21. C Note first that the triangles $P S T$ and $S Q T$ have the same perpendicular height. Hence the ratio of their areas is equal to the ratio of their bases. Therefore area of triangle $P S T: 18=2: 3$ and hence the area of triangle $P S T$ is 12. Similarly, triangles PSR and SQR have the same perpendicular height and hence $(12+20)$ : area of triangle $S Q R=2: 3$. Therefore the area of triangle $S Q R$ is $\frac{3}{2} \times 32=48$. Therefore the total area of triangle $P Q R$ is $12+20+48=80$.