Question

11.In the figure PQ is parallel to MN.If KP/PM=5/11 and KN=20cm then find the value of KQ .​

Answer 1

$\textbf{Given:}$

$\mathsf{In\;triangle\;ABC,\;PQ{\parallel}MN,\;\;\dfrac{KP}{PM}=\dfrac{5}{11},\;\;KN=20\;cm}$

$\textbf{To find:}$

$\textsf{The value of KQ}$

$\textbf{Solution:}$

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

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

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

$\mathsf{In\;\triangle\,KMN,}$

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

$\mathsf{\dfrac{KP}{PM}=\dfrac{KQ}{QN}}$

$\mathsf{\dfrac{KP}{PM}=\dfrac{KQ}{KN-KQ}}$

$\mathsf{\dfrac{KP}{PM}=\dfrac{KQ}{20-KQ}}$

$\mathsf{\dfrac{5}{11}=\dfrac{KQ}{20-KQ}}$

$\mathsf{5(20-KQ)=11\,KQ}$

$\mathsf{100-5\;KQ=11\,KQ}$

$\mathsf{100=16\,KQ}$

$\mathsf{KQ=\dfrac{100}{16}}$

$\mathsf{KQ=\dfrac{25}{4}}$

$\implies\boxed{\mathsf{KQ=6.25\;cm}}$

$\textbf{Answer:}$

$\textsf{Length of KQ is 6.25 cm}$

Find more:

In triangle abc, DE // BC and AD/DB = 3/5. If AC= 4.8 cm, find the AE.

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