(Q17).In which of the following situations, does the list of numbers involved in the form a G.P.?

(iii).Perimeter of the each triangle, when the mid-points of sides of an equilateral triangle whose side is 24 cm are joined to form another triangle, whose mid-points in turn are joined to form still another triangle and the process continues indefinitely.

24 cm24 cm24 cm

Given: An equilateral triangle whose perimeter = 24 cm.

Rate of annual increment = 10 %.

Side of the equilateral triangle =
= cm.

[∵ All sides of equilateral are equal] ……. (1)

Now each side of the triangle formed by joining the mid-points of the above triangle in step (1) =
= cm.

[∵ A line joining the mid-points of any two sides of a triangle is equal to half the third side.]

Similarly, the side of third triangle =
= cm.

∴ The sides of the triangles so formed are cm, cm, cm,

a =

a2
a1
 =
=
a3
a2
 =
=
Thus each term starting from the second; can be obtained by multiplying its preceding term by a fixed number

∴ The situation forms a G.P.