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

Explanation

Let the areas of two similar triangles be `A_(1)` and `A_(2)`. Let their respective corresponding sides be `s_(1)` and `s_(2)`. `A_(1)=225sqcm, A_(2)=81` sq. cm and `s_(2)=12cm`………….(Given)
The two triangles are similar.
`:.` by the theorem of areas of similar triangles,
`:.(A_(1))/(A_(2))=(s_(1)^(2))/(s_(2)^(2))`
`:.225/81=(s_(1)^(2))/(12^(2))`
`:.s_(1)^(2)=(225xx12^(2))/81`
`:.s_(1)=(15xx12)/9`
.................(Taking square roots on both the sides)
`:.s_(1)=20` cm
The corresponding side of the bigger triangle is 20 cm.