Question

A piece of string is 30 cm long. What will be the length of each side if the string is used to form : 

1. a square? 
2.  an equilateral triangle? 
3.  a regular hexagon?

Answer 1

\(\text{Length of string} = \text{Perimeter of each figure}\)

(a) Perimeter of square = \(30\) \(cm\) 
\(\Rightarrow 4 \times side = 30\) \(cm\) 
\(\Rightarrow Side = \frac{30}{ 4} =\) \(7.5\) \(cm\)

Thus, the length of each side of square is \(7.5\) \(cm\).

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(b)  Perimeter of equilateral triangle = \(30\) \(cm\) 
\(\Rightarrow 3 \times side = 30\) \(cm\)
\(\Rightarrow Side = \frac{30}{ 3} = 10 \;cm\)

Thus, the length of each side of equilateral triangle is \(10\) cm.

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(c)  Perimeter of hexagon = \(30\) \(cm\) 
\(\Rightarrow 6 \times side = 30\; cm\)
\(\Rightarrow Side = \frac{30}{ 6} = 5 \;cm\)

Thus, the side of each side of hexagon is \(5\) \(cm\)