Geometry: Similarities?

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2 Answers
Chirag Mehta
Mar 23, 2018

#RO=10#

Explanation:

paint, question

I assume that #angle1=angle2#
#therefore SQ||OP" "# (#angle1," "angle2" are corresponding angles"#)

Using Basic Proportionality Theorem or say BPT
#=>4/x=x/9#

#=>4*9=x*x#

#=>36=x^2#

#sqrt36=x#

#6=x" "# (x is length so, can't be negative)

#RO=4+x=4+6=10#

#color(purple)(RO=10#

CW
Mar 23, 2018

#RO=10# units

Explanation:

given #angleRSQ=angleROP, => DeltaRSQ and DeltaROP# are similar,
let #SO=RQ=x#,
#=> (RO)/(RS)=(RP)/(RQ)#
#=> (4+x)/4=(x+9)/(x)#
#=> 4x+x^2=4x+36#
#=> x^2=36#
#=> x=+-6#
as #x# can not be negative,
#=> x=6# units
#=> RO=4+x=4+6=10# units

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