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Question

A line segment CD has two points R and S such that CR:RD=2:3 and CS:SD=5:6.

Sort in ascending order of lengths.

A
RD
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B
CR
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C
SD
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D
CS
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Solution

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+1CR+RDRD=53CDRD=53RD=35CD(2)

From equation (1)
CR=23RD=23×35RD
=25CD(3)

CSSD=56(4)CSSD+1=56+1CS+SDSD=116CDSD=116SD=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

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