Here triangles CMX and CDS are similar. SO we use the ratio rule of similar triangles which states that the ratio of the corresponding sides are in same proportion . That is
![(SM)/(XD)=(CS)/(CX)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/4itjtwj3w5tx7hiu9rt7e1w1yrshf2rce4.png)
Let SX=x
![(7)/(9) = (15)/(15+x)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/3kmp0zwt1w96phdxnwj66fwfhne8f1isnq.png)
Doing cross multiplication
7(15+x) = 9*15
Distributing 7 on 15 +x ,
105 +7x = 135
Subtracting 105
7x=30
Dividing both sides by 7
x= 4.3
So CX=CS +SX = 15+4.3 = 19.3 or approx 20
Correct option is the first option .