Math, asked by simrandhaliwal1494, 3 months ago

if a point d devides line segment AB of length 10cm internally in the ratio 2:3 find the length of AD​

Answers

Answered by MaheswariS
1

\textbf{Given:}

\textsf{Point D divides line segment AB internally in the ratio 2:3}

\mathsf{and\;AB=10\;cm}

\textbf{To find:}

\textsf{Length of AD}

\textbf{Solution:}

\textsf{Since the point D divides AB internally in the ratio 2:3,}

\textsf{we have AD:DB=2:3}

\mathsf{\dfrac{AD}{DB}=\dfrac{2}{3}}

\mathsf{\dfrac{DB}{AD}=\dfrac{3}{2}}

\mathsf{\dfrac{DB}{AD}+1=\dfrac{3}{2}+1}

\mathsf{\dfrac{DB+AD}{AD}=\dfrac{3+2}{2}}

\mathsf{\dfrac{AB}{AD}=\dfrac{5}{2}}

\mathsf{\dfrac{10}{AD}=\dfrac{5}{2}}

\mathsf{\dfrac{2}{AD}=\dfrac{1}{2}}

\implies\mathsf{AD=2{\times}2}

\implies\boxed{\mathsf{AD=4\;cm}}

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