Brainlag Plus
Brainlag PlusSimilar shapes and scale factors
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.
Lengths scale by one factor
Similar shapes 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.
The rest of this lesson and its 10 practice questions are in Plus.
Screen 1 of 3, free to read.
- 10 exam-style questions, marked as you go, each with a worked solution
- Anything you get wrong is saved to your flashcards