Question

∆ABC and ∆XYZ are equilateral triangle BC=4cm, XY=12cm. the A(∆ABC) : A(∆XYZ) =​

Answer 1

Given : ∆ABC and ∆XYZ are equilateral triangle

BC=4cm, XY=12cm.

To Find :  Ar(∆ABC) : Ar(∆XYZ )

Solution:

All Equilateral triangles are similar

=> ∆ABC ≈ ∆XYZ

BC=4cm

XY = 12 cm => YZ = 12 cm as all the sides of Equilateral triangles are equal )

Ratio of area of similar triangle = ( ratio of corresponding sides)²

=> Ar(∆ABC) : Ar(∆XYZ )  =  ( BC/YZ)²

=>  Ar(∆ABC) : Ar(∆XYZ )  =  ( 4/12)²

=>  Ar(∆ABC) : Ar(∆XYZ )  =  ( 1/3)²

=>  Ar(∆ABC) : Ar(∆XYZ )  = 1/9

Ar(∆ABC) : Ar(∆XYZ )  = 1 : 9

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