Package of problems

Problem

Here are some triangles.

The diagrams are not to scale.

Can you find …

1. … a triangle similar to triangle A with perimeter $6$?

2. … a triangle similar to triangle B with perimeter $6$?

3. … a triangle similar to triangle C with perimeter $6$?

4. … a triangle similar to triangle D with perimeter $6$?

5. … a triangle similar to triangle A with area $10$?

6. … a triangle similar to triangle B with area $10$?

7. … a triangle similar to triangle C with area $10$?

8. … a triangle similar to triangle D with area $10$?

9. … a right-angled triangle similar to one of triangles A, B, C, D with area $12$?

10. … an isosceles triangle similar to one of triangles A, B, C, D with area $12$?

11. … an equilateral triangle similar to one of triangles A, B, C, D with area $12$?

12. … a scalene triangle similar to one of triangles A, B, C, D with area $12$?

13. … a right-angled triangle with area $12$ that is not similar to any of triangles A, B, C, D?

14. … an isosceles triangle with area $12$ that is not similar to any of triangles A, B, C, D?

15. … an equilateral triangle with area $12$ that is not similar to any of triangles A, B, C, D?

16. … a scalene triangle with area $12$ that is not similar to any of triangles A, B, C, D?