Question

In triangle ABC line DE parallel to side BC. AD=2,DB=6,EC=9.find AE. Which law do you applied to find AE.

Answer 1

$\textsf{We apply Thales theorem to find AE}$

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

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

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

$\textsf{Given: In \triangle ABC, DE{\parallel}AB}$

$\textsf{By Thales theorem, we have}$

$\displaystyle\mathsf{\frac{AD}{DB}=\frac{AE}{EC}}$

$\implies\displaystyle\mathsf{\frac{2}{6}=\frac{AE}{9}}$

$\implies\displaystyle\mathsf{\frac{1}{3}=\frac{AE}{9}}$

$\implies\displaystyle\mathsf{AE=\frac{9}{3}}$

$\implies\mathsf{AE=3}$

$\therefore\boxed{\textsf{AE= 3 units}}$

Find more:

Given DE parallel to BC AD=4.5 BD=9cm EC=8cm what is length of AE​

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