Ratio of similitude

The ratio of proportionality between similar figures. It is also sometimes called the dilation factor. If two plane figures are similar, then their corresponding sides are proportional. The ratio of the sides of one figure to the sides of the other figure is the ratio of similitude.

In the diagram below, the two triangles are similar. The ratio of similitude of the smaller to the larger is $\frac{2}{3}$, the ratio of the length of one of its sides to the corresponding side of the larger triangle.

Example:

If the length of the base of one rectangle is three times the length of the base of the other rectangle, then it follows that the other sides of the first rectangle are also three times longer than the sides of the second rectangle, giving a ratio of similitude of 3.

The perimeter of the first rectangle is also three times the perimeter of the second. The area of the first rectangle is nine times the area of the second, three times longer and three times wider.

In the diagram below, the two triangles are similar. The ratio of similitude of the smaller to the larger is $\frac{2}{3}$, the ratio of the length of one of its sides to the corresponding side of the larger triangle.

The perimeter of the first rectangle is also three times the perimeter of the second. The area of the first rectangle is nine times the area of the second, three times longer and three times wider.