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

In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues up to seven times. What is the ratio of the area of fourth triangle to that of seventh triangle? Correct Answer 64 : 1

Let the length of side of first equilateral triangle = x;

As shown in the figure, when an equilateral triangle is drawn inside another equilateral triangle joining the mid-points of the sides, the sides of that triangle will be half of the side of the 1st equilateral triangle;

: = 64 : 1

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