To determine the length of each side when a string of 30 cm forms different regular shapes, we need to divide the total length by the number of sides.

(a) Equilateral Triangle:

An equilateral triangle has 3 sides, and each side is equal in length.
$\text{Length of each side} = \frac{\text{Total length of string}}{\text{Number of sides}} = \frac{30}{3} = 10 \, \text{cm}.$

(b) Square:

A square has 4 equal sides.
$\text{Length of each side} = \frac{30}{4} = 7.5 \, \text{cm}.$

(c) Regular Hexagon:

A regular hexagon has 6 equal sides.
$\text{Length of each side} = \frac{30}{6} = 5 \, \text{cm}.$

Final Results:

• (a) Equilateral Triangle: 10 cm per side.
• (b) Square: 7.5 cm per side.
• (c) Regular Hexagon: 5 cm per side.

Would you like detailed explanations about geometric properties, or have any other questions?

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Related Questions:

1. How does the perimeter formula vary for polygons with unequal sides?
2. What are the interior angles of an equilateral triangle, square, and hexagon?
3. How would the results change if the string were 60 cm instead of 30 cm?
4. How can we use the concept of perimeter in real-world applications?
5. What is the area of these shapes if they are formed with the given side lengths?

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Tip:

For regular polygons, dividing the perimeter by the number of sides always gives the side length.