Given CR:RD=2:3 and CS:SD=5:6
Let us try to find all the line segments with respect to CD.
CRRD=23−−−(1)⇒CRRD+1=23+1⇒CR+RDRD=53⇒CDRD=53⇒RD=35CD−−−(2)
From equation (1)
⇒CR=23RD=23×35RD
=25CD−−−(3)
⇒CSSD=56−−−(4)⇒CSSD+1=56+1⇒CS+SDSD=116⇒CDSD=116⇒SD=611CD−−−(5)
From equation (4)
⇒CS=56SD=56×611CD
=511CD−−−(6)
From equations (1), (2), (3) and (4), converting all the segments to common denominator.
RD=3355CDCR=2255CDSD=3055CDCS=2555CD
Hence,
CR<CS<SD<RD