A sequence of equilateral triangles is drawn The altitude of each is root 3 times the altitude of the - Maths - Sequences and Series

Question

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:

10
12
16
18

Anuradha Sharma · Accepted Answer

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

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: 10 12 16 18

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:

10

12

16

18