Mathematics
The ratio between the areas of two similar triangles is 16 : 25. State the ratio between their :
(i) perimeters
(ii) corresponding altitudes
(iii) corresponding medians.
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Answer
We know that,
The ratio between the areas of two similar triangles is same as the square of the ratio between their corresponding sides.
Given,
Ratio between areas = 16 : 25.
So, ratio between sides = = 4 : 5.
(i) The ratio between the perimeters of two similar triangles is same as the ratio between their sides.
Hence, the required ratio = 4 : 5.
(ii) The ratio between the altitudes of two similar triangles is same as the ratio between their sides.
Hence, the required ratio = 4 : 5.
(iii) The ratio between the medians of two similar triangles is same as the ratio between their sides.
Hence, the required ratio = 4 : 5.
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