Question

A piece of string is $30cm$ long. What will be the length of each side if the string is used to form :
(a) a square ?
(b) an equilateral triangles ?
(c) a regular hexagon ?

Answer 1

Solution:-

The string length is the perimeter of the shape.

$\therefore$ For each case, $\text{perimeter}=30cm$

(i) Square

A square has all the side equal.

$\text{Perimeter}=4\times \left(\text{side of square}\right)$

$\therefore \text{side of square}=\frac{\text{perimeter}}{4}=\frac{30}{4}=7.5cm$

Hence, length of each side if the string is used to form a square will be 7.5 cm.

(ii) Equilateral triangle

An equilateral triangle has three equal sides.

$\text{Perimeter}=3\times \left(\text{side}\right)$

$\therefore \text{side}=\frac{perimeter}{3}=\frac{30}{3}=10cm$

Hence, length of each side if the string is used to form an equilateral triangle will be 10 cm.

(iii) Regular hexagon

A regular hexagon has six equal sides.

$\text{Perimeter}=6\times \left(\text{side}\right)$

$\therefore \text{side}=\frac{perimeter}{6}=\frac{30}{6}=5cm$

Hence, length of each side if the string is used to form a regular hexagon will be 5 cm.