A sequence of equilateral triangles is drawn. The altitude of each is root 3 times the altitude of the preceding triangle,the difference between the area of the first triangle and the sixth triangle is 968 root 3 square units. the perimeter of the first triangle is:
  1. 10
  2. 12
  3. 16
  4. 18

Let the altitude of first triangle is x and side of that equilateral triangle is a, So x= 32aNow sequencely  for secodn third , ..sixth triangle have altitude = 3a2, 33a2,9a2, 93a2, 27a2So side of first triangle = 2x3and side of 6th triangle = 2x27Now difference in area = 344x23-4x2272= 9683x213-1729=968242729x2=968x2=4×729x = 54So side of first triangle=2×543So perimeter of first triangle = 4×2×543 Regards

  • -27
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