Question

In the fig MN ||BC .If AM =5cm AN =10cm NC=16cm .calculate MB

Answer 1

$\textbf{Given:}$

$\text{In \triangle ABC, MN \parallel BC, AM=5 cm, AN=10 cm, NC=16 cm}$

$\textbf{To find:}$

$\text{Length of MB}$

$\textbf{Solution:}$

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

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

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

$\text{In \triangle ABC, apply Thales theorem}$

$\dfrac{AM}{MB}=\dfrac{AN}{NC}$

$\dfrac{5}{MB}=\dfrac{10}{16}$

$\dfrac{5}{MB}=\dfrac{5}{8}$

$\dfrac{1}{MB}=\dfrac{1}{8}$

$\implies\,MB=8\,\text{cm}$

$\therefore\textbf{Length of MB is 8 cm}$

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