Question

A rhombus has the same perimeter as the circumference of a circle. If the side length of the Thombosis 22
cm find the radius of the circle. (Take =)
Radius
A thesis of arrombus are equal​

Answer 1

Question :-

A rhombus has the same perimeter as the circumference of a circle. If the side of the Rhombus is 22 cm, then find the radius of the circle.

To Find :-

The Radius of the Circle.

Given :-

• Side of the Rhombus = 22 cm

We Know :-

Perimeter of a Rhombus :-

$\bf{\boxed{P = 4 \times s}}$

Circumference of a Circle :-

$\bf{\boxed{P = 2\pi r}}$

Where ,

• a = Equal Side of the Rhombus

• r = Radius of the circle.

• P = Perimeter

Concept :-

According to the question , the Perimeter of the Rhombus is equal to the Circumference of the Circle .

So by finding the Perimeter of the Rhombus and putting that value in the Formula for Circumference of the Circle , we can determine the value of Radius of Circle.

Solution :-

Perimeter of the Rhombus :-

$\:\:\:\:\:\:\:\:\:\:\:$Given length of the Rhombus is 22 cm.

Using the formula for Perimeter of a Rhombus , we get :

$\implies \bf{P = 4 \times s} \\ \\ \\ \implies \bf{P = 4 \times 22} \\ \\ \\ \implies \bf{P = 88 cm} \therefore \purple{\bf{P = 88 cm}}$

Hence, the Perimeter of the Rhombus is 88 cm.

Radius of the Circle :- [ π = 22/7]

ATQ :-

$\bf{P_{(Rhombus)} = P_{(Circle)}}$

Hence , "The Circumference of the Circle is also 88 cm".

Using the formula for Circumference of a Circle and by substituting the value in it , we get :-

$\implies \bf{P = 2\pi r} \\ \\ \\ \implies \bf{88 = 2 \times \dfrac{22}{7} \times r} \\ \\ \\ \implies \bf{\dfrac{88}{2} = \dfrac{22}{7} \times r} \\ \\ \\ \implies \bf{44 = \dfrac{22}{7} \times r} \\ \\ \\ \implies \bf{44 \times 7 = 22 \times r} \\ \\ \\ \implies \bf{\dfrac{44 \times 7}{22} = r} \\ \\ \\ \implies \bf{2 \times 7 = r} \\ \\ \\ \implies \bf{14 cm = r} \\ \\ \\ \therefore \purple{\bf{r = 14 cm}}$

Hence , the Radius of the Circle is 14 cm.

Answer 2

Answer:

Given the side of a rhombus = 22 m

We know that the perimeter of the rhombus = 4 x side = 4 x 22 m

= 88 m.

According to the question it is clear that,

Perimeter of the rhombus = Circumference of the circle 88 = 2 π r 88

= 2 × (22/7) × r r

=(88 × 7)/ 44 r = 616/44 r

= 14 m

Therefore radius of the circle = 14m