Question

Areas of two similar triangles are 225 sq.cm. 81 sq.cm. If a side of the smaller triangle is 12 cm, then Find corresponding side of the bigger triangle.

Answer 1

Let areas of two similar triangles be A₁ and A₂ & their corresponding sides be S₁ and S₂

A₁ = 225 sq.cm, A₂ = 81 sq.cm

S₂ = 12 cm, S₁ = ? 

`"A"_1/"A"_2="S"_1^2/"S"_2^2`   ...[Theorem of areas of similar triangle]

`225/81="S"_1^2/(12)^2`

Taking square root on both side

`sqrt(225/81)=sqrt("S"_1/12)`

`15/9="S"_1/12`

`15/9xx12="S"_1`

∴ S₁ = 20 cm