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The length of a rectangle is three-fifths of the side of a square. The radius of a circle is equal to the 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 8 cm?
- a)112.4 sq. cm
- b)104.2 sq. cm
- c)100.8 sq. cm
- d)Cannot be determined
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Given information:
- The length of a rectangle is three-fifths of the side of a square.
- The breadth of the rectangle is 8 cm.
- The radius of a circle is equal to the side of the square.
- The circumference of the circle is 132 cm.
Let's solve the problem step by step:
Step 1: Determine the radius of the circle.
The circumference of a circle is given by the formula:
C = 2πr, where C is the circumference and r is the radius.
In this case, we are given that the circumference of the circle is 132 cm.
So, 132 = 2πr.
Dividing both sides by 2π, we get:
r = 132 / (2π) ≈ 21 cm.
Step 2: Determine the side of the square.
We are given that the radius of the circle is equal to the side of the square.
Therefore, the side of the square is also 21 cm.
Step 3: Determine the length of the rectangle.
We are given that the length of the rectangle is three-fifths of the side of the square.
So, the length of the rectangle is (3/5) * 21 = 63/5 = 12.6 cm.
Step 4: Determine the area of the rectangle.
The area of a rectangle is given by the formula:
A = length * breadth.
In this case, the length is 12.6 cm and the breadth is 8 cm.
Therefore, the area of the rectangle is 12.6 * 8 = 100.8 square cm.
Therefore, the correct answer is option (c) 100.8 sq. cm.
- The length of a rectangle is three-fifths of the side of a square.
- The breadth of the rectangle is 8 cm.
- The radius of a circle is equal to the side of the square.
- The circumference of the circle is 132 cm.
Let's solve the problem step by step:
Step 1: Determine the radius of the circle.
The circumference of a circle is given by the formula:
C = 2πr, where C is the circumference and r is the radius.
In this case, we are given that the circumference of the circle is 132 cm.
So, 132 = 2πr.
Dividing both sides by 2π, we get:
r = 132 / (2π) ≈ 21 cm.
Step 2: Determine the side of the square.
We are given that the radius of the circle is equal to the side of the square.
Therefore, the side of the square is also 21 cm.
Step 3: Determine the length of the rectangle.
We are given that the length of the rectangle is three-fifths of the side of the square.
So, the length of the rectangle is (3/5) * 21 = 63/5 = 12.6 cm.
Step 4: Determine the area of the rectangle.
The area of a rectangle is given by the formula:
A = length * breadth.
In this case, the length is 12.6 cm and the breadth is 8 cm.
Therefore, the area of the rectangle is 12.6 * 8 = 100.8 square cm.
Therefore, the correct answer is option (c) 100.8 sq. cm.
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The length of a rectangle is three-fifths of the side of a square. The radius of a circle is equal to the 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 8 cm?a)112.4 sq. cmb)104.2 sq. cmc)100.8 sq. cmd)Cannot be determinede)None of theseCorrect answer is option 'C'. Can you explain this answer?
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