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InterviewSolution
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Areas of two similar triangles are 100 cm2 and 64 cm2. If the median of bigger triangle is 10 cm, then the median of the smaller triangle is …………(A) 10 cm (B) 6 cm (C) 4 cm (D) 8 cm |
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Answer» 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 |
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