Find the sum of areas of all the triangles. (a) 4A/5 (b) 4A/3 (c) 3A/4 (d) 5A/4

Question

The middle points of the sides of a triangle are joined forming a second triangle. Again a third triangle is formed by joining the middle points of this second triangle and this process is repeated infinitely. If the perimeter and area of the outer triangle are P and A respectively, 

Find the sum of areas of all the triangles. 

(a) 4A/5 

(b) 4A/3

(c) 3A/4 

(d) 5A/4 

Answer 1

Correct option 4A/3

Explanation: 

The areas would be A + A/4 + A/16 +…till infinite terms. The infinite sum of all the perimeters would be 4A/3.