In an equilateral triangle another equilateral triangle is drawn inside joining the mid points of th...........

Quantitative Aptitude (CDS) Mensuration 2D

In an equilateral triangle another equilateral triangle is drawn inside joining the mid-points of the sides of given equilateral triangle and the process is continued up to 7 times. What is the ratio of area of fourth triangle to that of seventh triangle?

256 : 1

128 : 1

64 : 1

16 : 1

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Explanation:

Here all triangles are equilateral triangle and formed after taking the mid-point of sides.
Let Area of ΔABC be A then Area of nth triangle (??_n)=(1/4)ⁿA …….. (i)
According to question,

Hence, A₄:A₇=64:1
Hence option (3)