Every side of a triangle is increased by 30 per cent, producing a triangle similar to the original.
By what percentage does the area increase?

The length factor is 1.30, so the area factor is $1.30^2=1.69$. The new area is 169 per cent of the old, an increase of $169-100=69$ per cent. Answering 30 per cent quotes the length increase, 60 per cent merely doubles it, and 169 per cent gives the new area as a percentage of the old rather than the increase.