Question

If the altitude of two similar triangles are in the ratio 2 : 3, what is the ratio of their areas?

Answer 1

Answer:

The ratio of the areas of two triangles is 4: 9.

Step-by-step explanation:

Given:

The corresponding altitudes of two similar triangles are 2 cm and 3 cm.

 We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.

 ar(∆1/)ar(∆2) = (altitude1/ altitude2)²

 ar(∆1)/ar(∆2) = (2/3)²

 ar(∆1)/ar(∆2) = 4/9

 ar(∆1) : ar(∆2) = 4: 9

 Hence, the ratio of the areas of two triangles is 4: 9.

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Answer 2

Solution:-

Given:-

Ratio of Altitude of two similar Triangle = 2:3

To Find:-

Ratio of their Areas = ?

Find:-

We know that,

The Ratio of similar Triangle is equal to the Ratio of the Square of Corresponding sides as well as their corresponding Altitudes.

=) (Area of ∆a)/(Area of ∆b) = (Altitude 1)²/(Altitude 2)²

=) (Area of ∆a)/(Area of ∆b) = (2/3)²

=) (Area of ∆a)/(Area of ∆b) = 4/9

=) (Area of ∆a) : (Area of ∆b) = 4 : 9

Hence,

Ratio of the Areas of the similar Triangle is 4 : 9.