Question

In ∆ABC, A - P - B ∧  B- Q - C, if PQ || AC BP = 6, PA = 8, BQ = 9 then QC = ____​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{In triangle ABC,}$

$\mathsf{PQ\,\parallel\,AC,BP=6,\,PA=8,\,BQ=9}$

$\underline{\textsf{To find:}}$

$\textsf{Length of QC}$

$\underline{\textsf{Solution:}}$

$\underline{\mathsf{Thale's theorem:}}$

$\textsf{If a line is drawn parallel to one side of a triangle, then}$

$\textsf{cuts other two sides proportionally}$

$\mathsf{Apply\;Thale's\;theorem\;in\;\triangle\,ABC,we\;get}$

$\mathsf{\dfrac{BP}{AP}=\dfrac{BQ}{QC}}$

$\implies\mathsf{\dfrac{6}{8}=\dfrac{9}{QC}}$

$\implies\mathsf{\dfrac{3}{4}=\dfrac{9}{QC}}$

$\implies\mathsf{\dfrac{1}{4}=\dfrac{3}{QC}}$

$\implies\mathsf{QC=4{\times}3}$

$\implies\boxed{\mathsf{QC=12\;cm}}$

$\underline{\textsf{Answer:}}$

$\mathsf{Length\;of\;QC\;is\;12\;cm}$

$\underline{\textsf{Find more:}}$

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Answer 2

Answer:

answer is 12 centimeter