Rudraksh cuts off three equilateral triangles, of sides 2cm each, from the three corners of a bigger equilateral triangle what will be the perimeter of the new shape as compared to the original triangle

The resulting hexagon has a perimeter 6 cm shorter than the original equilateral triangle.

For an equilateral triangle, each angle equals 60°.

For a regular hexagon, each angle equals 120°.

So, ∠IHG = 120° and ∠CHG = 180 - 120 = 60°

ABC is the equilateral triangle and so ∠C = 60°

Now, ∠CGH will be 60° and triangle CHG is also an equilateral triangle. Hence CH=HG=CG

Similarly we can infer that all sides are equal (AD=DE=EB=FB=GF=EF=GH=HI=ID=IA=CH=CG)

So, HI=2cm

AC = CH + HI + IA = 2 +2 +2 = 6cm

The perimeter of new shape = DE + EF + FG + GH + HI = 12 cm

The perimeter of equilateral triangle ABC = 18 cm

Therefore, The resulting hexagon has a perimeter 6 cm shorter than the original equilateral triangle.

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  The resulting hexagon will have perimeter 6 cm shorter.

Step-by-step explanation:

Each cut reduces the perimeter by 2 cm, so the three cuts together reduce it by ...

  3 · (2 cm) = 6 cm

The resulting hexagon has a perimeter 6 cm shorter than the original equilateral triangle.

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In the attached diagram, we show the original perimeter portion (red) and the new perimeter portion (blue). Note that the blue segment is 2 cm shorter than the sum of the lengths of the red segments. Hence, the new perimeter is 2 cm shorter than the original. This is repeated at each of the 3 corners of the original triangle.

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