Question

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?

Answer 1

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 `triangle ABC` put 6cm side corresponding to 12cm side.
Let `triangle ABC ~ triangle DEF`

6cm side corresponding to 12 cm side .
therefore, `(AB)/(DE)=(BC)/(EF)=(CA)/(FD)=1/2`
So the perimeter of ABC is half of the perimeter of DEF .
perimeter of DEF = `2×(3+4+6)=2×13=26cm`
answer 26 cm.

Answer 2

`26cm`

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 `Delta ABC,` the sides are `" "3" ":" "4" ":" "6`

For the smallest perimeter of the other triangle, the longest side must be `12`cm. The sides will therefore all be twice as long.

`Delta ABC:" "3" ":" "4" ":" "6`
New `Delta:" "6" ":" "8" ":" "12`

The perimeter of `Delta ABC = 6+4+3 = 13cm`

The perimeter of the second triangle will be `13xx2 = 26cm`

This can be confirmed by adding the sides:

`6+8+12 = 26cm`