Question

A piece of wire is 48 cm long.what will be the length of each side if the wire is used to form:
a) an equilateral triangle
b) a square
c) a regular hexagon​

Answer 1

Answer:-

$\small \bf \underline{Given:}$

★★ Length of the piece of wire or perimeter of all the figures = 48cm

$\small \bf \underline{To \: find:}$

We need to find the length of each side if the wire is used to form :

a) an equilateral triangle

b) a square

c) a regular hexagon

$\small \bf \underline{Solution:}$

a) Let a be the length of each side of an equilateral triangle

Formula to find the perimeter of an equilateral triangle = 3a

Therefore, according to the question the equation formed is as follows :-

$\bf \: 3a = 48$

$\bf \implies \: a = \frac{48}{3}$

$\bf \implies \: a = 16cm$

Answer: The length of each side of an equilateral triangle = 16cm

b) Let a be the length of each side of a square

Formula to find the perimeter of a square = 4a

Therefore, according to the question the equation formed is as follows :-

$\bf \: 4a = 48$

$\bf \implies \: a = \frac{48}{4}$

$\bf \implies \: a = 12cm$

Answer: The length of each side of a square = 12cm

c) Let a be the length of each side of a regular hexagon

Formula to find the perimeter of a regular hexagon = 6a

Therefore, according to the question the equation formed is as follows :-

$\bf \: 6a = 48$

$\bf \implies \: a = \frac{48}{6}$

$\bf \implies \: a = 8cm$

Answer: The length of each side of a regular hexagon = 8cm

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Answer 2

Answer:

The length of each side if the string is used to form a square is 12 cm.

The length of each side if the string is used to form an equilateral triangle is 16 cm.

The length of each side if the string is used to form a regular hexagon is 8 cm.

Step-by-step explanation:

Given : A piece of string is 48 cm long.

To find : What will be the length of each side if the string is used to form a square, an equilateral triangle, a regular hexagon ?

Solution :

If the string is used to form a square,

The perimeter of the square is P=4aP=4a

where, P=48 cm is perimeter

a is the length of side.

48=4a48=4a

a=\frac{48}{4}a=

4

48

a=12\ cma=12 cm

The length of each side if the string is used to form a square is 12 cm.

If the string is used to form an equilateral triangle,

The perimeter of the an equilateral triangle is P=3aP=3a

where, P=48 cm is perimeter

a is the length of side.

48=3a48=3a

a=\frac{48}{3}a=

3

48

a=16\ cma=16 cm

The length of each side if the string is used to form an equilateral triangle is 16 cm.

If the string is used to form a regular hexagon,

The perimeter of the a regular hexagon is P=6aP=6a

where, P=48 cm is perimeter

a is the length of side.

48=6a48=6a

a=\frac{48}{6}a=

6

48

a=8\ cma=8 cm

The length of each side if the string is used to form a regular hexagon is 8 cm.