Question

In Δ ABC, DE || BC, AD = 4 cm, AB = 9 cm, AC = 13.5 cm then the value of EC is​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{In\;\triangle,\;DE\parallel\,BC,\;AD=4\,cm,\;AB=9\,cm,\;AC=13.5\,cm}$

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

$\textsf{The value of EC}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Basic proportionality theorem:}}$

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

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

$\mathsf{In\;\triangle\;ABC,\;by\;BPT}$

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

$\mathsf{\dfrac{4}{5}=\dfrac{13.5-EC}{EC}}$

$\mathsf{4\,EC=67.5-5\,EC}$

$\mathsf{9\,EC=67.5}$

$\mathsf{EC=\dfrac{67.5}{9}}$

$\implies\boxed{\mathsf{EC=7.5\,cm}}$

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

In ∆ABC, PQ||AB. If AP=10cm. PC=8cm, QC=12cm. then find BQ

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