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The circumference of a circle is equal to the perimeter of a rectangle whose length and breadth are in ratio 4:3, respectively. If the area of the rectangle is 5808 cm2 , then find the radius of the circle.
  • a)
    28 cm
  • b)
    52.5 cm
  • c)
    22 cm
  • d)
    49 cm
  • e)
    50.5 cm
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The circumference of a circle is equal to the perimeter of a rectangl...
To find the radius of the circle, we need to consider the relationship between the circumference of the circle and the perimeter of the rectangle.

Let's assume that the length of the rectangle is 4x and the breadth is 3x, where x is a constant.

- Perimeter of the rectangle:
Perimeter = 2(Length + Breadth)
Perimeter = 2(4x + 3x) = 14x

- Circumference of the circle:
Circumference = 2πr, where r is the radius of the circle.

According to the problem, the perimeter of the rectangle is equal to the circumference of the circle. Therefore, we have:
14x = 2πr

- Area of the rectangle:
Area = Length × Breadth
5808 = 4x × 3x
5808 = 12x^2

Now, we have two equations:
14x = 2πr ---- (1)
5808 = 12x^2 ---- (2)

To find the value of x, we can solve equation (2) for x:
12x^2 = 5808
x^2 = 5808/12
x^2 = 484
x = √484
x = 22

- Calculating the radius:
Substituting the value of x in equation (1), we can find the radius of the circle:
14(22) = 2πr
308 = 2πr
r = 308/2π
r = 154/π

Approximating the value of π to 3.14:
r ≈ 154/3.14
r ≈ 49 cm

Therefore, the radius of the circle is approximately 49 cm.
Hence, the correct answer is option D.
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Community Answer
The circumference of a circle is equal to the perimeter of a rectangl...
Let the length and breadth of the rectangle be 4x cm and 3x cm, respectively
According to the question,
4x × 3x = 5808
=> x2 = 5808/12 = 484
=> x = 22
Therefore, perimeter of the rectangle = 2 × (4x + 3x) = 308 cm
Let the radius of the circle be ‘r’ cm
According to the question,
2?r = 308
Or, r = 308 × (7/44) = 49 cm
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The circumference of a circle is equal to the perimeter of a rectangle whose length and breadth are in ratio 4:3, respectively. If the area of the rectangle is 5808 cm2 , then find the radius of the circle.a)28 cmb)52.5 cmc)22 cmd)49 cme)50.5 cmCorrect answer is option 'D'. Can you explain this answer?
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