Question

Area of circle is equal to the area of a rectangle having perimeter of 50 cms. and length more than the breadth by 3 cms. What is the diameter of the circle?

A) 7 cms B) 21 cms C) 28 cms D) 14 cms

Answer 1

Given :-

Area of the circle = Area of the rectangle

Perimeter of the rectangle = 50 cm

Length of the rectangle exceeds the breadth by 3 cm

Required to find :-

• Diameter of the circle ?

Formulae used :-

$\dagger{\boxed{\tt{ Perimeter \ of \ the \ rectangle = 2 ( length + breadth ) }}}$

$\dagger{\boxed{\tt{ Area \ of \ the \ rectangle = length \times breadth }}}$

$\dagger{\boxed{\tt{Area \ of \ the \ circle = \pi {r}^{2} }}}$

Solution :-

Given information :-

Area of the circle = Area of the rectangle

Perimeter of the rectangle = 50 cm

Length of the rectangle exceeds the breadth by 3 cm

We need to find the diameter of the circle

So,

Let's consider

The breadth of the rectangle = x cm

Length of the rectangle exceeds by 3 cm = x + 3 cm

Perimeter of the rectangle = 50 cm

According to problem ;

2 ( length + breadth ) = 50 cm

2 ( x + 3 + x ) = 50

2 ( 2x + 3 ) = 50

2x + 3 = 50/2

2x + 3 = 25

2x = 25 - 3

2x = 22

x = 22/2

x = 11 cm

Hence,

Length of the rectangle = x + 3 = 11 + 3 = 14 cm

Breadth of the rectangle = x = 11 cm

Using the formula ;

$\dagger{\boxed{\tt{ Area \ of \ the \ rectangle = length \times breadth }}}$

Area of the rectangle = length x breadth

Area of the rectangle = 14 cm x 11 cm

Area of the rectangle = 154 cm²

However,

It is also given that ;

Area of the circle = Area of the rectangle

Hence,

Area of the circle = 154 cm²

Let,

The radius of the circle be " r " cm

Using the formula ;

$\dagger{\boxed{\tt{Area \ of \ the \ circle = \pi {r}^{2} }}}$

According to the problem ;

$\tt{ \dfrac{22}{7} \times r \times r = 154 }$

$\tt{ \dfrac{22}{7} \times {r}^{2} = 154 }$

$\tt{ {r}^{2} = 154 \times \dfrac{7}{22} }$

$\tt{ {r}^{2} = 7 \times 7 }$

$\tt{ {r}^{2} = 49 }$

$\tt{ r = \sqrt{49} }$

$\tt{ r = +7 \ or \ - 7}$

Since, radius can't be in negative .

Hence,

Radius of the circle = r = 7 cm

We know that

Diameter is 2 times the radius

So,

Diameter = 2 x radius

Diameter = 2 x 7 cm

Diameter = 14 cm

Therefore

Diameter of the circle = 14 cm

Conclusion :-

• Option - D is correct

Diagrams :-

$\setlength{\unitlength}{10}{\begin{picture}(0,0) \put(0,1){\line(0,1){5.5}}\put(0,1){\line(1,0){7}}\put(7,1){\line(0,1){5.5}}\put(0,6.5){\line(1,0){7}}\put(1,0){ \tt Length = 14 cm }\put(7.2,3.5){ \tt Breadth = 11 cm }\put(1,7){ \tt Rectangle }\end{picture}}$

$\setlength{\unitlength}{20}{\begin{picture}(0, 0)\put(2,2){\circle{14}} \put(1,2){\line(1, 0){2}}\put(2,2){\line(1, - 1){0.75}} \put(2,2.1){ \tt c }\put(2,2.1){ \tt c }\put(2.4,1.6){ \tt r }\put(2.5,1.5){\vector(1, -0){2}}\put(4.6,1.5){ \tt r = 7cm }\put(2,2){\vector(1,1){1}} \put(3.3,3.1){ \tt diameter = 14 \: cm }\put(6,2.2){ \tt c \: = centre }\end{picture}}$

Answer 2

GIVEN:

• Area of circle = Area of rectangle .

• Perimeter of rectangle = 50 cm .

• Length is 3cm more tha the breadth.

TO FIND:

• Diameter of the circle.

SOLUTION:

Let, the breadth be x cm .

so, length become ( x + 3) cm .

Perimeter of rectangle = 50 cm

=> 2 ( l + b) = 50

=> 2 ( x + 3 + x ) = 50

=> 2 ( 3 + 2x ) = 50

=> 6 + 4x = 50

=> 4x = 50 - 6

=> 4x = 44

=> x = 44 / 4

=> x = 11

Therefore, length = x + 3 = 11 + 3 = 14 cm

Therefore, breadth = x = 11 cm

Now,

Area of rectangle = Length × breadth

= 14cm × 11cm

= 154 cm²

A.T.Q

Area of circle = 154 cm²

=> pi r² = 154 cm²

=> 22/7 × r² = 154

=> r² = ( 154 × 7 ) / 22

=> r² = 7 × 7

=> r = ✔49

=> r = 7 cm

As we know that,

Diameter = 2r

= 2 × 7

= 14 cm

Therefore, the diameter of circle is 14 cm..

Hence , option ( D ) is correct.