Geometry: Similarities?

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2 Answers
Mar 23, 2018

RO=10

Explanation:

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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

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