UPSC 2016 CDS II Math Paper

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