Question

4
the correct alternatives of the following
1) The areas of two similar triangle are 36cm and 8
cm. The ratio of their
corresponding height is
a) 9:16 b) 6:9 c) 36:81​

Answer 1

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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