Question

The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.

Answer 1

SOLUTION :  

Given:

The corresponding altitudes of two similar triangles are 6 cm and 9 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) = (6/9)²

ar(∆1)/ar(∆2) = 36/81

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 two similar triangle = 6cm and 9cm

$<b>$Area of two similar triangle is equal to area of their square of corresponding angle

so we do like this

( Altitude / altitude of triangle)² = 6/9

we square both the aides as we get

( altitude of 1/ altitude of 2) =(6/9)²

( Altitude of 1./ Altitude of 2)= 36 / 81


(Alt1./ Alt2 )= 4/9

Ratio of two similar triangle are

4:9