Similar perimeter
What are the possible perimeters of the larger triangle?
Age
14 to 16
Challenge level
Problem
The lengths of the sides of a triangle A are 3, 4, and 6.
Triangle B is similar to triangle A. One of the sides of triangle B has length 12.
What are the possible perimeters that triangle B could have?
This problem is taken from the World Mathematics Championships
Student Solutions
To get a side length of 12,
- the side of length 3 could be enlarged by a scale factor of 4
or - the side of length 4 could be enlarged by a scale factor of 3
or - the side of length 6 could be enlarged by a scale factor of 2
The perimeter of triangle A is 3 + 4 + 6 = 13, so the possible perimeters of triangle B are:
12 + 16 + 24 = 52 (following an enlargement by a scale factor of 4)
or
9 + 12 + 18 = 39 (following an enlargement by a scale factor of 3)
or
and 6 + 8 + 12 = 26 (following an enlargement by a scale factor of 2)