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The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side 22 cm. What is the breadth of the rectangle, if its perimeter is 668 cm?
- a)24 cm
- b)26 cm
- c)52 cm
- d)Cannot be determined
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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The length of a rectangle is twice the diameter of a circle. The circu...
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The length of a rectangle is twice the diameter of a circle. The circu...
Given information:
- The length of the rectangle is twice the diameter of the circle.
- The circumference of the circle is equal to the area of a square with a side length of 22 cm.
- The perimeter of the rectangle is 668 cm.
To find: The breadth of the rectangle.
Let's solve this step by step:
Step 1: Find the diameter of the circle
The circumference of the circle is equal to the perimeter of the square, which is 4 * side length.
So, the circumference of the circle = 4 * 22 = 88 cm.
The circumference of a circle is given by the formula: circumference = π * diameter.
Therefore, π * diameter = 88 cm.
Dividing both sides of the equation by π, we get: diameter = 88 / π cm.
Step 2: Find the length of the rectangle
The length of the rectangle is twice the diameter of the circle.
Therefore, length = 2 * diameter = 2 * (88 / π) cm.
Step 3: Find the breadth of the rectangle
The perimeter of the rectangle is given as 668 cm.
Perimeter of a rectangle = 2 * (length + breadth).
Substituting the values, we have: 668 = 2 * (2 * (88 / π) + breadth).
Simplifying the equation, we get: 668 = (176 / π) + 2 * breadth.
Rearranging the equation, we have: 2 * breadth = 668 - (176 / π).
Dividing both sides by 2, we get: breadth = (668 - (176 / π)) / 2.
Calculating the value of breadth using a calculator, we find:
breadth ≈ 26 cm.
Therefore, the breadth of the rectangle is approximately 26 cm, which is option B.
- The length of the rectangle is twice the diameter of the circle.
- The circumference of the circle is equal to the area of a square with a side length of 22 cm.
- The perimeter of the rectangle is 668 cm.
To find: The breadth of the rectangle.
Let's solve this step by step:
Step 1: Find the diameter of the circle
The circumference of the circle is equal to the perimeter of the square, which is 4 * side length.
So, the circumference of the circle = 4 * 22 = 88 cm.
The circumference of a circle is given by the formula: circumference = π * diameter.
Therefore, π * diameter = 88 cm.
Dividing both sides of the equation by π, we get: diameter = 88 / π cm.
Step 2: Find the length of the rectangle
The length of the rectangle is twice the diameter of the circle.
Therefore, length = 2 * diameter = 2 * (88 / π) cm.
Step 3: Find the breadth of the rectangle
The perimeter of the rectangle is given as 668 cm.
Perimeter of a rectangle = 2 * (length + breadth).
Substituting the values, we have: 668 = 2 * (2 * (88 / π) + breadth).
Simplifying the equation, we get: 668 = (176 / π) + 2 * breadth.
Rearranging the equation, we have: 2 * breadth = 668 - (176 / π).
Dividing both sides by 2, we get: breadth = (668 - (176 / π)) / 2.
Calculating the value of breadth using a calculator, we find:
breadth ≈ 26 cm.
Therefore, the breadth of the rectangle is approximately 26 cm, which is option B.
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The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side 22 cm. What is the breadth of the rectangle, if its perimeter is 668 cm?a)24 cmb)26 cmc)52 cmd)Cannot be determinede)None of theseCorrect answer is option 'B'. Can you explain this answer?
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