Here are two similar right-angled triangles: triangle 𝑎 and triangle 𝑏. Write the ratio of side 𝑎 to side 𝑏. 𝑎 to 𝑏 equals what?
To help us find the ratio, we can compare the length of the sides of each triangle. The base of triangle 𝑎 is two squares, and the length of the base of triangle 𝑏 is eight squares. The height of triangle 𝑎 is one square, and the height of triangle 𝑏 is four squares.
The height of triangle 𝑏 is four times the height of triangle 𝑎 because one multiplied by four is four. So the triangles have been drawn to a scale factor of four. The height of triangle 𝑏 is four times the height of triangle 𝑎. And the base of triangle 𝑏 is four times the base of triangle 𝑎 because two multiplied by four is eight.
This means that side 𝑏 marked on the triangle is four times the length of side 𝑎. So the ratio of 𝑎 to 𝑏 is one to four. We could also write this as two to eight. Both answers are correct.