Enlargements and scale factors

problem

Golden Triangle

Age

16 to 18

Challenge level

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.
problem

Sierpinski Triangle

Age

16 to 18

Challenge level

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.
problem

Squareflake

Age

16 to 18

Challenge level

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.
problem

Similar Rectangles

Age

14 to 16

Challenge level

Can you find the missing length?
problem

Scale Draw

Age

5 to 7

Challenge level

Use the grids to draw pictures to different scales.
problem

Scaling Clowns

Age

5 to 7

Challenge level

These five clowns work in pairs. What is the same and what is different about each pair's faces?
problem

Conical Bottle

Age

14 to 16

Challenge level

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?
problem

Matter of Scale

Age

14 to 16

Challenge level

Can you prove Pythagoras' Theorem using enlargements and scale factors?
problem

L-Triominoes

Age

14 to 16

Challenge level

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
problem

Flower Show

Age

14 to 16

Challenge level

How long will it take six gardeners to dig six circular flower beds?