The figure below is formed by 3 big identical equilateral triangles and 3 small identical equilateral triangles. The length of GH is 54 cm. What is the perimeter of the figure?

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Worked solution

13

1. Relate the bases of the triangles to the length of GH

The sum of the bases of the 6 equilateral triangles is equal to the length of GHGH, which is 5454 cm.

2. Relate the perimeter of the figure to the bases

Each equilateral triangle has 33 equal sides. One side lies on GHGH, and the other 22 sides contribute to the perimeter of the figure. Thus, the perimeter of the figure is 22 times the sum of the bases.

3. Calculate the perimeter

Perimeter=2×54=108 cm\text{Perimeter} = 2 \times 54 = 108 \text{ cm}

Answer

108108 cm

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