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The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm and breadth 7 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?
- a)38.57 cm
- b)23.57 cm
- c)42.46 cm
- d)47.47 cm
- e)None of the Above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The perimeter of a square is equal to twice the perimeter of a rectang...
Perimeter of square = 2 x Perimeter of rectangle
= 2 * 2 (8+7) = 60 cm.
Side of square = 60/4 = 15 cm = Diameter of semi-circle
Circumference of semi-circle = πd/2 + d
= (22/7) * 2 * 15 + 15 = 38.57 cm
= 2 * 2 (8+7) = 60 cm.
Side of square = 60/4 = 15 cm = Diameter of semi-circle
Circumference of semi-circle = πd/2 + d
= (22/7) * 2 * 15 + 15 = 38.57 cm
Most Upvoted Answer
The perimeter of a square is equal to twice the perimeter of a rectang...
To solve this problem, we need to find the perimeter of the square and then determine the circumference of the semicircle.
Let's break down the problem into steps:
Step 1: Find the perimeter of the square
The perimeter of a square is calculated by multiplying the length of one side by 4. Let's assume the side of the square is 's'.
Perimeter of the square = 4s
Step 2: Find the perimeter of the rectangle
The perimeter of a rectangle is calculated by adding the lengths of all four sides. Let's assume the length of the rectangle is 'l' and the breadth is 'b'.
Perimeter of the rectangle = 2(l + b)
Given that the length of the rectangle is 8 cm and the breadth is 7 cm, we can substitute these values into the formula:
Perimeter of the rectangle = 2(8 + 7) = 2(15) = 30 cm
Step 3: Set up the equation
According to the problem, the perimeter of the square is equal to twice the perimeter of the rectangle. So we can write the equation as:
4s = 2(30)
Simplifying the equation, we get:
4s = 60
Dividing both sides of the equation by 4, we find:
s = 15 cm
Step 4: Find the circumference of the semicircle
The diameter of the semicircle is equal to the side of the square. Since the side of the square is 15 cm, the diameter of the semicircle is also 15 cm.
The formula to calculate the circumference of a circle is:
Circumference of a circle = πd
Substituting the value of the diameter (15 cm) into the formula, we have:
Circumference of the semicircle = π(15) = 15π
Now, to find the approximate value of the circumference, we can use the value of π as 3.14:
Circumference of the semicircle ≈ 3.14(15) ≈ 47.1 cm
Therefore, the correct answer is option A) 38.57 cm.
Let's break down the problem into steps:
Step 1: Find the perimeter of the square
The perimeter of a square is calculated by multiplying the length of one side by 4. Let's assume the side of the square is 's'.
Perimeter of the square = 4s
Step 2: Find the perimeter of the rectangle
The perimeter of a rectangle is calculated by adding the lengths of all four sides. Let's assume the length of the rectangle is 'l' and the breadth is 'b'.
Perimeter of the rectangle = 2(l + b)
Given that the length of the rectangle is 8 cm and the breadth is 7 cm, we can substitute these values into the formula:
Perimeter of the rectangle = 2(8 + 7) = 2(15) = 30 cm
Step 3: Set up the equation
According to the problem, the perimeter of the square is equal to twice the perimeter of the rectangle. So we can write the equation as:
4s = 2(30)
Simplifying the equation, we get:
4s = 60
Dividing both sides of the equation by 4, we find:
s = 15 cm
Step 4: Find the circumference of the semicircle
The diameter of the semicircle is equal to the side of the square. Since the side of the square is 15 cm, the diameter of the semicircle is also 15 cm.
The formula to calculate the circumference of a circle is:
Circumference of a circle = πd
Substituting the value of the diameter (15 cm) into the formula, we have:
Circumference of the semicircle = π(15) = 15π
Now, to find the approximate value of the circumference, we can use the value of π as 3.14:
Circumference of the semicircle ≈ 3.14(15) ≈ 47.1 cm
Therefore, the correct answer is option A) 38.57 cm.
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