The length of a rectangle is 3/5th of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle, if the breadth of the rectangle is 15 cm?
Question
The length of a rectangle is 3/5th of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle, if the breadth of the rectangle is 15 cm?
Solution
Sure, let's solve this step by step:
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First, we know that the circumference of a circle is given by the formula 2πr, where r is the radius of the circle. We are given that the circumference is 132 cm. So, we can set up the equation 2πr = 132 to solve for r.
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Solving the above equation for r, we get r = 132 / (2π) = 21 cm (approximately).
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We are told that the radius of the circle is equal to the side of the square. So, the side of the square is also 21 cm.
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The length of the rectangle is 3/5th of the side of the square. So, the length of the rectangle is 3/5 * 21 = 12.6 cm.
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We are given that the breadth of the rectangle is 15 cm.
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The area of a rectangle is given by the formula length * breadth. So, the area of the rectangle is 12.6 cm * 15 cm = 189 cm².
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