Resources tagged with: Enlargements and scale factors

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There are 14 results

Broad Topics > Transformations and constructions > Enlargements and scale factors

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.

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.

The Rescaled Map

Age 14 to 16
Challenge Level

We use statistics to give ourselves an informed view on a subject of interest. This problem explores how to scale countries on a map to represent characteristics other than land area.

Von Koch Curve

Age 16 to 18
Challenge Level

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

Circles Ad Infinitum

Age 16 to 18
Challenge Level

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

Matter of Scale

Age 14 to 16
Challenge Level

Prove Pythagoras' Theorem using enlargements and scale factors.

Squirty

Age 14 to 16
Challenge Level

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

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.

Fit for Photocopying

Age 14 to 16
Challenge Level

Explore the relationships between different paper sizes.

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?

Similar Rectangles

Age 14 to 16
Challenge Level

Can you find the missing length?

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?

Arrow Arithmetic 1

Age 14 to 16
Challenge Level

The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.

Fill Me up Too

Age 14 to 16
Challenge Level

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?