2016 · Q56
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 ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A256 : 1
- B128 : 1
- C64 : 1
- D16 : 1
Explanation
Each mid-point triangle has 1/4 the area of its parent. From the 4th to the 7th triangle the area shrinks by (1/4)³ = 1/64. So the ratio of the fourth triangle's area to the seventh's is 64:1 (option C).