Question

The area of two triangles with same Base are 9cmsq and 16cm sq . Find the ratio of their corresponding heights.

Answer 1

Given

Area of two triangles = 9 cm² & 16 cm²

Base of two triangles = Equal

To find

Ratio of corresponding height

Solution

Here, areas are given as 9 cm² & 16 cm²

Base₁ = Base₂

We know that,

➥ Area of ∆ = ½ × Base × Height

Putting values :

⟿ ½ × Base₁ × Height₁ = 9 -(Eq.1)

⟿ ½ × Base₂ × Height₂ = 16 -(Eq.2)

Now dividing both equations :

➝ ½ × Base × Height₁/ ½ × Base × Height₂ = 9/16

• Cancelling out (½ × Base) from both

➝ Height₁ / Height₂ = 9/16

➝ Height₁ : Height₂ = 9 : 16

Therefore,

Ratio of corresponding heights = 9 : 16