Question

The lengths of the sides of a square are multiplied by 2.5, How is the ratio of the areas related to the ratio of the sides?

Answer 1

What is the ratio for a square?

Answer 2

On what you know

Answer 3

Generally it's a square
(that's why we call squaring squaring)

Answer 4

If you double both sides of the square, you can fit four normal squares inside the new square. If you triple both sides, you can fit nine normal squares inside the new square. And so forth

Answer 5

Does this make sense in the 2.5 case?

Answer 6

If you multiply a side of the square by any number, the area of the square will increase by the 'square' of that same number.

In the first case:
\[Area= x ^{2}\]
whereas in the second case:
\[Area=(2.5x)(2.5x)=(2.5\times2.5)(x timesx)=2.5^{2}timesx ^{2}\]