Ratio and proportion

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?

Show that it is rare for a ratio of ratios to be rational.

Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.

Move the point P to see how P' moves. Then use your insights to calculate a missing length.

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

Use the grids to draw pictures to different scales.

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.