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.