The lengths of the sides of a square are multiplied by 1.2. How is the ratio of the areas related to the ratio of the side lengths?

The ratio of the areas is equal to the ratio of the lengths squared

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor and the ratio of its areas is equal to the scale factor squared

In this problem

If the lengths of the sides of a square are multiplied by 1.2

then

the scale factor is 1.2

Remember that the ratio of the side lengths is equal to the scale factor

so

The ratio of the side lengths is equal to 1.2

and

The ratio of the areas is equal to the scale factor squared

so

The ratio of the areas is equal to 1.2^2

therefore

The ratio of the areas is equal to the ratio of the lengths squared