Point S is on line segment \overline{RT} RT . Given ST=2x,ST=2x, RT=4x,RT=4x, and RS=4x-4,RS=4x−4, determine the numerical length of \overline{RS}. RS .

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Jferard asked Nov 5, 2023

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32 votes

Point S is on line segment \overline{RT}

RT
. Given ST=2x,ST=2x, RT=4x,RT=4x, and RS=4x-4,RS=4x−4, determine the numerical length of \overline{RS}.
RS
.

Mathematics
college

Jferard asked Nov 5, 2023

by Jferard

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1 Answer

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$\underset{\leftarrow \qquad \textit{\LARGE 4x}\qquad \to }{R\stackrel{4x-4}{\rule[0.35em]{7em}{0.25pt}} S\stackrel{2x}{\rule[0.35em]{20em}{0.25pt}}T} \\\\\\ RT~~ - ~~ST~~ = ~~RS\implies \stackrel{RT}{4x} - \stackrel{ST}{2x}~~ = ~~\stackrel{RS}{4x-4} \\\\\\ -2x=-4\implies x=\cfrac{-4}{-2}\implies \boxed{x=2}~\hfill \stackrel{4(2)~~ - ~~4}{RS=8}$