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​

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

Radius = 14/2

Radius = 7

Radius of circular wire is 7 cm.

Put r in circumference formula :

Circumference = 2 × 22/7 × 7

Circumference = 308/7

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

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

44 = [2 × (4.5 + 5.5)] + x + x

44 = 20 + 2x

44 - 20 = 2x

24 = 2x

x = 24/2

x = 12

Perimeter of Square is 12 cm.

So, For side :

12 = 4 × side

12/4 = side

side = 3

Therefore,

Length of side of Square is 3 cm.

Step-by-step explanation:

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