Question

In ∆ RST, line PQ || side ST, R-P-S and R-Q-T, RP = 4, PS = 6, RQ = 3. Find QT.

Answer 1

$\textbf{Given:}$

$\text{In \triangle RST, PQ \parallel ST, RP=4, PS=6, RQ=3}$

$\textbf{To find:}$

$\text{Length of QT}$

$\textbf{Solution:}$

$\textbf{Basic proportionality theorem(Thales theorem):}$

$\text{If a line is drawn parallel to one side of a}$

$\text{triangle then it cuts other two sides proportionally.}$

$\text{In \triangle RST, by Thales theorem}$

$\dfrac{RP}{PS}=\dfrac{RQ}{QT}$

$\dfrac{4}{6}=\dfrac{3}{QT}$

$\dfrac{2}{3}=\dfrac{3}{QT}$

$\implies\,QT=\dfrac{9}{2}$

$\implies\bf\,QT=4.5\,text{cm}$

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