Question

Triangles ABC and DEF are similar. The perimeter of triangle ABC is 23. The perimeter of triangle DEF is twice as large as triangle ABC. What are the possible lengths of triangle DEF.

Answer 1

Since ABC and DEF are similar, with ratio 1:2, it means that the sides of DEF are twice the size of ABC.

So, the perimeter of DEF is twice the perimeter of ABC, which means it is 46.

We can't pick any triplet of numbers that sum to 46 anyway, because in every triangle the sum of two sides must exceed the third one.

So, for example, the sides of DEF can't be 1, 5, 40, because 1+5 < 40.

A good option (although there are infinite possibility) could be for example 15, 11 and 20.