The ratio of corresponding sides of similar triangles is `3 : 5`, then what is the ratio of their areas.

Explanation

Let the corresponding sides of two similar triangles be `s_(1)` and `s_(2)`. Let their respective areas be `A_(1)` and `A_(2)`.
`s_(1):s_(2)=3:5`……………(Given)
`:.(s_(1))/(s_(2))=3/5`……….1
The two triangles are similar.
`:.(A_(1))/(A_(2))=(s_(1)^(2))/(s_(2)^(2))`
..........(Theorem of area of similar triangles)
`:.(A_(1))/(A_(2))=((s_(1))/(s_(2)))^(2)`
`:.(A_(1))/(A_(2))=(3/5)^(2)` .............[From 1]
`:.(A_(1))/(A_(2))=9/25`
`:.A_(1):A_(2)=9:25`
The ratio fo the areas of two similar triangles is `9:25`.