Question

A circular wire of diameter 14 cm is re-bent to forma parallelogram, a square, and a rhombus.The sides of the parallelogram are 4.5cm and 5.5cm. Also,the square and the rhombus have equal sides.Find the side length of the square.

Need step by step explanation/solution

pls help​

Answer 1

Answer:

• Length of side of Square is 3 cm.

Step-by-step explanation:

Given :-

• Diameter of circular wire is 14 cm.
• Sides of parallelogram are 4.5 cm and 4.5 cm.
• Sides of Square and rhombus are equal.

To find :-

• Length of side of Square.

Solution :-

Circumference/Perimeter of circle = 2πr

Where, r is radius

Radius = Diameter/2

$\rightarrow$ Radius = 14/2

$\rightarrow$ Radius = 7

Radius of circular wire is 7 cm.

Put r in circumference formula :

$\longrightarrow$ Circumference = 2 × 22/7 × 7

$\longrightarrow$ Circumference = 308/7

$\longrightarrow$ Circumference = 44

Circumference of circle is 44 cm

Circumference of circle will be the length of wire.

Length of circular wire is 44 cm.

Now,

So, Circumference/Perimeter of circle = Perimeter of parallelogram + Perimeter of Square + Perimeter of rhombus

If rhombus and square have equal sides than there Perimeter will be same.

Let, Perimeter of Square be x

$\longrightarrow$ 2πr = [2 × (l + b + [4 × side] + [4 × side]

$\longrightarrow$ 44 = [2 × (4.5 + 5.5)] + x + x

$\longrightarrow$ 44 = 20 + 2x

$\longrightarrow$ 44 - 20 = 2x

$\longrightarrow$ 24 = 2x

$\longrightarrow$ x = 24/2

$\longrightarrow$ x = 12

Perimeter of Square is 12 cm.

So, For side :

$\longrightarrow$ 12 = 4 × side

$\longrightarrow$ 12/4 = side

$\longrightarrow$ side = 3

Therefore,

Length of side of Square is 3 cm.

Answer 2

Answer:

Given :-

• A circular wire of diameter is 14 cm is re-bent to form a parallelogram, a square, and a rhombus. The sides of the parallelogram are 4.5 cm and 5.5 cm. Also, the square and the rhombus have equal sides.

To Find :-

• What is the side of length of the square.

Formula Used :-

$\sf\boxed{\bold{\pink{Circumference\: of\: Circle =\: 2{\pi}r}}}$

where,

• r = Radius

$\sf\boxed{\bold{\pink{Perimeter\: of\: Square =\: 4(Side)}}}$

Solution :-

First, we have to find the radius of a circular wire :

As we know that,

$\sf\bold{Radius =\: \dfrac{Diameter}{2}}$

Given :

• Diameter = 14 cm

Then,

↦ $\sf Radius =\: \dfrac{\cancel{14}}{\cancel{2}}$

➙ $\sf\bold{\purple{Radius =\: 7\: cm}}$

Hence, the radius of a circular wire is 7 cm.

Now, we have to find the circumference of a circle,

Given :

• Radius = 7 cm

Then,

↦ $\sf Circumference\: of\: Circle =\: 2 \times \dfrac{22}{\cancel{7}} \times {\cancel{7}}$

↦ $\sf Circumference\: of\: Circle =\: 2 \times 22$

➦ $\sf\bold{\green{Circumference\: of\: Circle =\: 44\: cm}}$

Hence, the circumference of a circle is 44 cm.

We can say that circumference of a circle is a length of a circle.

Again, we have to find the side of length of the square,

Given :

• Perimeter = 44 cm

According to the question by using the formula we get,

⇒ $\sf 4(Side) =\: 44$

⇒ $\sf 4 \times Side =\: 44$

⇒ $\sf Side =\: \dfrac{\cancel{44}}{\cancel{4}}$

➠ $\sf\bold{\red{Side =\: 11\: cm}}$

$\therefore$ The side of length of the square is 11 cm.

➲ Some Important Formula :-

➤ Formula related to circle :

$\leadsto$ $\sf Diameter\: of\: Circle =\: 2 \times r$

$\leadsto$ $\sf Area\: of\: Circle\: =\: {\pi}{r}^{2}$

where,

• r = Radius

➤ Formula related to square :

$\leadsto$ $\sf Area\: of\: Square =\: {a}^{2}$

$\leadsto$ $\sf Perimeter\: of\: Square =\: 4a$

$\leadsto$ $\sf Diagonal\: of\: Square =\: \sqrt{2}a$

where,

• a = Length of a side of the square.