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

Correct option is D

We are given that the area of a circle is equal to the area of a rectangle, where:

• The perimeter of the rectangle is 50 cm.

• The length of the rectangle is 3 cm more than its breadth.

We need to find the diameter of the circle.

Step 1: Find the Length and Breadth of the Rectangle

The formula for the perimeter of a rectangle is:

2 (L + B) = 50

Since the length is 3 cm more than the breadth, we can write:

L = B + 3

Substituting into the perimeter equation:

2 (B + 3 + B) = 50

2 (2B + 3) = 50

4B + 6 = 50

4B = 44

$$B = 11, \quad L = 11 + 3 = 14$$​

The area of the rectangle is:

​$$\text{Area} = L \times B = 14 \times 11 = 154 \text{ cm}^2$$​

Step 3: Equate to the Area of the Circle

The area of a circle is given by:

​$$\pi r^2 = 154$$​

​$$\pi as \frac{22}{7} , we get:$$​​

​$$\frac{22}{7} r^2 = 154$$​

Multiplying both sides by 7:

​$$22r^2 = 1078$$​

Dividing by 22:

​$$r^2 = 49$$​

​$$r = \sqrt{49} = 7 \text{ cm}$$​

Step 4: Find the Diameter

The diameter of the circle is:

​$$D = 2r = 2 \times 7 = 14 \text{ cm}$$​

Final Answer:

​$$\boxed{14 \text{ cm}}$$​