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