Equilateral triangle is a triangle in which all its sides are equal.
Given:
side = 10 cm
Area of an equilateral triangle = √3/4 a²
1st: a = 10 ; A = 43.3 cm²
2nd: a = 5 ; A = 10.83 cm²
3rd: a = 2.5 ; A = 2.71 cm²
4th: a = 1.25 ; A = 0.68 cm²
5th: a = 0.625 ; A = 0.17 cm²
6th: a = 0.3125; A = 0.042 cm²
7th: a = 0.15625; A = 0.011.cm²
Summation: a1/1 -r ; a1 = 43.30 ; r = 0.25
43.30 / 1 - 0.25 = 43.30/0.75 = 57.73 cm²
The sum of the areas of the triangles if the process is continued without end is 57.73 cm²
Take a look at the attachment, but the answer is
5x^3 / 4y^3.
81x^2 - 4y^2 Note this is the difference of 2 perfect squares
a^2 - b^2 = (a + b)(a - b)
so here we have a = 9x and b = 2y
and our factors are
(9x + 2y)(9x - 2y)
the dimensions are 9x + 2y and 9x - 2y
( 6 + ( 2 * x ) -3) = 2x + 3