Question

The ratio between the areas of two similar triangles is 64 : 49. Find the ratio between their corresponding altitudes.

Answer 1

For similar triangles,

`"Area"_1/"Area"_2 = ("corresponding side"_1/"corresponding side"_2)^2`

Given,

Area ratio = 64 : 49

So,

`("side"_1/"side"_2)^2 = 64/49`

`"side"_1/"side"_2 = sqrt(64/49)`

`"side"_1/"side"_2 = 8/7`

In similar triangles, all corresponding linear measures (such as altitudes) are in the same ratio as corresponding sides.

∴ Ratio of altitudes = 8 : 7