Use ratio with similar shapes and solids: lengths, perimeters and scale models, similar triangles from a parallel line or a shared angle, and (Higher) the area and volume ratios that come from a length ratio.
What you will learn
- Find a length scale factor from lengths or perimeters and use it
- Use a scale such as 1 : 50 between a model and the real object
- Use similar triangles, including a parallel line that splits two sides in the same ratio
- Tell similar from congruent triangles
- Go between length, area and volume ratios (Higher)
Lengths scale by one factor
Shapes that are mathematically similar (similar, for short) are the same shape: every length is multiplied by the same scale factor, and the angles do not change.
Perimeters are lengths, so they scale by the same factor.
- two similar pentagons have perimeters 24 cm and 36 cm
- scale factor = 36 ÷ 24 = 1.5
- a 10 cm side on the small one matches 10 × 1.5 = 15 cm on the large one
A scale of 1 : 50 is a length ratio: every real length is 50 times the model length. Change units at the end: a 30 cm model is 30 × 50 = 1500 cm = 15 m long.
Going from real to model, divide: a real 6 m door is 600 cm, and 600 ÷ 50 = 12 cm on the model. Change the real length to centimetres first.
The rest of this lesson and its 10 practice questions are locked.
In this lesson
- Lengths scale by one factor
- Similar triangles in ratio problems
- Areas and volumes (Higher)
10 practice questions, marked as you go; about 30 minutes in all.
Key terms
Mathematically similar, Same scale factor, Parallel, Whole, Congruent, And, Hypotenuse, Square root, Cube root
In this unit: Ratio, gradients, similarity and growth
More ratio: one quantity as a fraction of another, ratio notation with units, ratios as linear functions, gradients as rates, similar shapes through length, area and volume ratios, and repeated percentage change.
- Fractions, ratio notation and linear functions
- Gradients as rates
- Similar shapes and scale factors
- Repeated proportional change