# The lengths of the sides of triangle ABC are 3 cm, 4cm, and 6 cm. How do you determine the least possible perimeter of a triangle similar to triangle ABC which has one side of length 12 cm?

##### 2 Answers

26cm

#### Explanation:

we want a triangle with shorter sides (smaller perimeter) and we got 2 similar triangles , since triangles are similar the **corresponding sides** would be in ratio.

To get triangle of shorter perimeter we have to use the longest side of

Let

6cm side corresponding to 12 cm side .

therefore,

So the perimeter of ABC is half of the perimeter of DEF .

perimeter of DEF =

answer 26 cm.

#### Explanation:

Similar triangles have the same shape because they have the same angles.

They are of different sizes, but their sides are in the same ratio.

In

For the smallest perimeter of the other triangle, the longest side must be

New

The perimeter of

The perimeter of the second triangle will be

This can be confirmed by adding the sides: