Question

The length of three sides of triangle ABC are 6cm, 4cm, and 9cm. Triangle DRF is similar to triangle ABC. The length of one of the sides of triangle DEF is 36 cm. What is greatest perimeter possible for triangle DEF?

Answer 1

Since ΔABC ~ ΔDEF
All sides of both triangles are similar.
Smallest side of ΔABC = 4cm
Ratio of the sides of the triangles = 4/36 = 1/9 = 1:9
Second side = 6×9 = 54cm
Third side = 9×9 = 81cm
Greatest perimeter possible = 36 + 54 + 81 = 171cm

Answer 2

Triangle DRF is similar to Triangle ABC.

So, To get the largest perimeter, then you need to make the smallest side of the second triangle be 36 (so the other sides are longer).

smallest side of the first triangle = 4

The smallest side of the second triangle = 36

Ratio of the sides of the triangle = 4/39
                                                   = 1/9 = 1:9

Each of the other sides of the larger triangle will be 9 times the similar side of the smaller one.
     first side = 36
     second side = 6 x 9 = 54
    third side   9 x 9 = 81 

Perimeter = 36 + 54 + 81
                =  171

so, the possible greatest perimeter for triangle DEF is 171.