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4 the correct alternatives of the following1) The areas of two similar triangle are 36cm and 8cm. The ratio of theircorresponding height isa) 9:16 b) 6:9 c) 36:81 |
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Answer» ong>Answer: 6 : 9 (Option b) Step-by-step EXPLANATION: Let the areas of the two triangles be A₁ and A₂. Let the heights of the two triangles be h₁ and h₂. Let ONE side of the first triangle be s₁ and its corresponding side in the second triangle be s₂. Given, ratios of areas of triangles = A₁ : A₂ = 36 : 81 We know that the areas of SIMILAR triangles are in the same ratio as the squares of their corresponding sides. So, A₁ : A₂ = s₁² : s₂² = 36 : 81 --------> ( I ) We know that the corresponding sides of similar triangles are in the same ratio as their corresponding heights. So, s₁ : s₂ = h₁ : h₂ --------------------------> ( II ) From ( I ), ( II ), s₁² : s₂² = h₁² : h₂² = 36 : 81 h₁² : h₂² = 36 : 81 h₁ : h₂ = √36 : √81 = 6 : 9 ∴ Ratio of corresponding heights of triangles = 6 : 9 (Option b) |
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