Question

In triangle ABC, DE||BC. If AD= 2.5cm, DB=5cm AE=3cm,and EC=x cm find the value of x

Answer 1

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

$\textsf{In triangle ABC,}\;\mathsf{DE\,\parallel\,BC}$$\mathsf{AD=2.5\,cm,\;DB=5\,cm,\;AE=3\,cm,\;EC=x\,cm}$

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

$\textsf{The value of 'x'}$

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

$\textsf{We apply Basic proportionality theorem to solve}$

$\textsf{the problem}$

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

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

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

$\textsf{In triangle ABC,}\;\mathsf{DE\,\parallel\,BC}$

$\textsf{By Basic proportionality theore, we have}$

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

$\mathsf{\dfrac{2.5}{5}=\dfrac{3}{x}}$

$\mathsf{\dfrac{1}{2}=\dfrac{3}{x}}$

$\implies\mathsf{x=2\times\,3}$

$\implies\boxed{\mathsf{x=6\,cm}}$

$\underline{\textbf{Answer:}}$

$\textsf{The value of x is 6 cm}$

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

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

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