Question

if the altitudes of two similar triangles are in the ratio 2 : 3, find their ratio of their areas and also the ratio of their corresponding medians.

Answer 1

Answer:

ratio of their corresponding sides = 3 : 5

we know, if two triangles are similar then, ratio of their corresponding sides = ratio of their corresponding medians = ratio of their corresponding altitudes

here given, ratio of corresponding medians of two similar triangles is 3 : 5.

so, ratio of their corresponding sides will be also 3 : 5 .

[ note : ratio of area of two similar triangles = square of ratio of their corresponding sides = square of ratio of their corresponding medians ]

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how to prove that ratio of corrosponding sides is the same as the ratio of ccorresponding medians in the similar triangle