The ratio between the areas of two similar triangles is 16 : 25, Find

1.	The ratio between the areas of two similar triangles is 16 : 25, Find the ratio between their:(i) perimeters (ii) altitudes(iii) medians
Answer» The ratio between the areas of two similar triangles is same as the square of the ratio between their corresponding sides. So, the ratio between the sides of the two triangles = 4 : 5 (i) The ratio between the perimeters of two similar triangles is same as the ratio between their sides. ∴ Required ratio = 4 : 5 (ii) The ratio between the altitudes of two similar triangles is same as the ratio between their sides. ∴ Required ratio = 4 : 5 (iii) The ratio between the medians of two similar triangles is same as the ratio between their sides. ∴ Required ratio = 4 : 5

The ratio between the areas of two similar triangles is 16 : 25, Find the ratio between their:(i) perimeters (ii) altitudes(iii) medians

Answer»

The ratio between the areas of two similar triangles is same as the square of the ratio between their corresponding sides.

So, the ratio between the sides of the two triangles = 4 : 5

(i) The ratio between the perimeters of two similar triangles is same as the ratio between their sides.

∴ Required ratio = 4 : 5

(ii) The ratio between the altitudes of two similar triangles is same as the ratio between their sides.

∴ Required ratio = 4 : 5

(iii) The ratio between the medians of two similar triangles is same as the ratio between their sides.

∴ Required ratio = 4 : 5

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