Areas of two similar triangles are 100 cm^2 and 64 cm^2. If the median of bigger triangle is 10 cm, then the median of the smaller triangle is ……

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 \(=10\times\frac8{10}=8\,cm\)

Correct option is: (D) 8 cm