Could someone please help me find the length?

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Answer 1 · 2018-06-26T08:50:28

#color(blue)(X=12)#

enter image source here

From diagram:

#/_TPR =/_STRcolor(white)(888)# ( alternate segment theorem )

#/_PRT=/_TRScolor(white)(888)# ( common angle )

Therefore:

#DeltaPRT~DeltaSTR color(white)(888)# (AA similarity )

#:.#

#(PR)/(TR)=(TR)/(SR)#

#18/X=X/8#

#X^2=144+>X=12#

Taking only positive root.

This is really just proving:

#PRxxSR=X^2#

Which we weren't allowed to use directly.