Mathematics
Grade9
Easy

Question

If triangles ABC and DEF are similar and AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, the perimeter of triangle is,

  1. 22 cm
  2. 20 cm
  3. 21 cm
  4. 18 cm

hintHint:

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar. Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.

The correct answer is: 18 cm


    ABC tilde DEF
AB equals 4 cm comma DE equals 6 cm comma EF equals 9 cm text  and  end text FD equals 12 cm
AB divided by DE equals BC divided by EF equals AC divided by DF

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 4 divided by 6 equals BC divided by 9 equals AC divided by 12 end cell row cell BC equals left parenthesis 4.9 right parenthesis divided by 6 equals 6 cm end cell row cell AC equals left parenthesis 12.4 right parenthesis divided by 6 equals 8 cm end cell end table

    text  Perimeter  end text equals A B plus B C plus A C

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals 4 plus 6 plus 8 end cell row cell equals 18 cm end cell end table

    We know that , perimeter of a triangle is the sum of all sides of a triangle.

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