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In triangle $\Delta ABC$, $AB=2\text{ cm}$, $BC=3\text{ cm}$, $CA=4\text{ cm}$. $D$ is the midpoint of $AC$. If a square is constructed on the side $BD$,what is the area of the square. Now i used similarity between $\Delta ABD$ and $\Delta BCD$ but to no result..

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1 Answer 1

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All you need is to find the length of the median $BD$. You can derive the following median formula using Cosine Law.

$$ \begin{align} &M_b=\frac{1}{2}\sqrt{2c^2+2a^2-b^2} \\\Rightarrow\ &BD=\frac{\sqrt{10}}{2} \\\Rightarrow\ &{\square}_{Area}=\frac{5}{2} \end{align} $$

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  • $\begingroup$ it it will be 10/4 so 5/2.... $\endgroup$
    – Pole_Star
    Jan 15, 2017 at 11:45
  • $\begingroup$ @dp1611 Rectified. $\endgroup$
    – 8hantanu
    Jan 15, 2017 at 11:46

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