Question

ABC में DE || BC तथा AD = 3 सेमी., DB = 5 सेमी, AE= 6 सेमी. है, तो EC का मान ज्ञात
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कीजिए।
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Answer 1

$\textbf{Given:}$

$\text{In \triangle ABC, DE \parallel AD, AD=3\,cm , DB=5\,cm , AE=6\,cm }$

$\textbf{To find:}$

$\text{Length of EC}$

$\textbf{Solution:}$

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

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

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

$\text{Since DE{\parallel}BC in\; \triangle ABC, by Thales theorem}$

$\dfrac{AD}{DB}=\dfrac{AE}{EC}$

$\dfrac{3}{5}=\dfrac{6}{EC}$

$\dfrac{1}{5}=\dfrac{2}{EC}$

$\implies\,EC=2{\times}5$

$\implies\,EC=10\,cm$

$\textbf{Answer:}$

$\textbf{Length of EC is 10 cm}$

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