Correct option is (D) 8 cm
Since, the areas of two similar triangles are in the ratio of the squares of their corresponding medians.
\(\therefore\) \(\frac{\text{Area of bigger triangle}}{\text{Area of smaller triangle}}\) \(=(\frac{\text{median of bigger triangle}}{\text{median of smaller triangle}})^2\)
\(\therefore\) \((\frac{10}{\text{median of smaller triangle}})^2=\frac{100}{64}\)
\(\Rightarrow\) \(\frac{10}{\text{median of smaller triangle}}=\sqrt{\frac{100}{64}}\)
\(=\frac{\sqrt{100}}{\sqrt{64}}=\frac{10}{8}\)
\(\therefore\) Median of smaller triangle \(=10\times\frac8{10}=8\,cm\)
