Using scale factors

Scale factors describe how much a shape has been enlarged (made larger).

Enlarging by a scale factor of 2 means that each side of the shape has been multiplied by 2.

All the sides double in length and the shape will be twice as large.

In the image below the purple square A has been enlarged by a scale factor of 2 to make the green square B.

Put your knowledge of scale factors to the test with this quiz. Then complete the rest of the page and see if you can beat your score.

Using a grid can help you understand scale factors. It makes it easier to see how much a shape grows when you enlarge it.

Here is a rectangle.

It has a width of 2 squares and a length of 4 squares.

If you wanted to make the rectangle twice the size, you would multiply the width by 2 and the length by 2.

For the width calculate:

2 squares × 2 = 4 squares

For the length calculate:

4 squares × 2 = 8 squares

Here is the enlarged rectangle.

This rectangle has a width of 4 squares and a length of 8 squares.

The shape has been enlarged by a scale factor of 2.

You could also say that the rectangle has doubled in size.

Enlarging by a scale factor using multiplication

Here is a triangle.

To enlarge it by a scale factor of 3, you need to multiply the dimensions by 3.

First, multiply the height:

5cm × 3 = 15cm

Then, multiply the length:

4cm × 3 = 12cm

Here is the triangle enlarged by a scale factor of 3.

The height is now 15cm and the length is now 12cm.

Finding the original size by using a scale factor

When a shape has been enlarged by a scale factor, you can work backwards to find its original size by doing the inverse (opposite) calculation - division.

The green rectangle B has been enlarged by a scale factor of 3 and now has a width of 9cm and a length of 12cm.

Let’s work out the original dimensions of the purple rectangle A.

To work out its original dimensions divide the new width by the scale factor:

9cm ÷ 3 = 3cm

Then, divide the new length by the scale factor:

12cm ÷ 3 = 4cm

So, the original rectangle had a width of 3cm and a length of 4cm before it was enlarged.

Investigate how different scale factors enlarge shapes with this interactive activity.