The mid-points of the sides of a triangle are joined forming a second triangle. Again, a third triangle is formed by joining the mid-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. What will be the sum of perimeters of all the triangles?
Explanation:
The length of sides of successive triangles will form a G.P. with common ratio 1/2. [Basic Proportionality Theorem]
∴ Total perimeter = P + P/2 + P/4 + … ∞
⇒ Total perimeter = P/(1 - 1/2) = 2P
Hence, option (a).
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