Let ΔA1B1C1is an equilateral triangle with side a units. Remember: We know that the line joining the midpoints of two sides of a triangle is parallel to the third side and half of it. ∴ΔA2B2C2 is an equilateral triangle with side
a
2
units Again ΔA3B3C3 is an equilateral triangle with side
(
a
2
)
2
=
a
22
Similarly, the sides of the fourth equilateral triangle so formed are
a
23
units and the sides of the seventh equilateral triangle so formed are
a
26
units. ∴
Area of the fourth triangle
Area of the seventh triangle
=
√3
4
×(
a
23
)2
√3
4
×(
a
26
)2
=26=64 Thus, the ratio of area of fourth triangle to that of seventh triangle is 64 : 1