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The length of a rectangle is 4/7 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 176 cm. What is the area of the rectangle if the breadth of the rectangle is 12 cm ?
- a)326 cm2
- b)352 cm2
- c)288 cm2
- d)336 cm2
- e)192 cm2
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
The length of a rectangle is 4/7 of the side of a square. The radius ...
Given
Length of rectangle is 4/7 of the side of square.
The radius of circle is equal to the side of the square.
Circumference of the circle is 176 cm.
Breadth of the rectangle is 12 cm.
Formula Used:
Circumference of circle =2πr
Area of rectangle = length × breadth
Let the radius of circle be x cm.
According to the question,
Side of square = Radius of square
Now, 2πr=176
⇒r=28 cm
⇒ Side of square =28 cm
⇒ Length of rectangle
= (4/7)×28=16 cm
Breadth of rectangle =12 cm
∴ Area of rectangle =16×12=192 cm2
Hence, the correct option is (E).
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The length of a rectangle is 4/7 of the side of a square. The radius ...
Understanding the Problem
To solve for the area of the rectangle, we need to determine the dimensions of the rectangle based on the information provided about the square and the circle.
Step 1: Find the Radius of the Circle
- The circumference of the circle is given as 176 cm.
- The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
where \( r \) is the radius.
- Rearranging the formula to find the radius:
\[ r = \frac{C}{2\pi} = \frac{176}{2\pi} \]
\[ r = \frac{88}{\pi} \]
Step 2: Determine the Side of the Square
- According to the problem, the radius of the circle is equal to the side of the square (s):
\[ s = r = \frac{88}{\pi} \]
Step 3: Find the Length of the Rectangle
- The length (L) of the rectangle is \( \frac{4}{7} \) of the side of the square:
\[ L = \frac{4}{7}s = \frac{4}{7} \times \frac{88}{\pi} \]
\[ L = \frac{352}{7\pi} \]
Step 4: Calculate the Area of the Rectangle
- The area (A) of the rectangle is given by:
\[ A = L \times \text{breadth} \]
- The breadth of the rectangle is provided as 12 cm:
\[ A = \left(\frac{352}{7\pi}\right) \times 12 \]
\[ A = \frac{4224}{7\pi} \]
Step 5: Approximate the Area
- Using \( \pi \approx 3.14 \):
\[ A \approx \frac{4224}{21.98} \approx 192 \text{ cm}^2 \]
Thus, the area of the rectangle is 192 cm². The correct answer is option 'E'.
To solve for the area of the rectangle, we need to determine the dimensions of the rectangle based on the information provided about the square and the circle.
Step 1: Find the Radius of the Circle
- The circumference of the circle is given as 176 cm.
- The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
where \( r \) is the radius.
- Rearranging the formula to find the radius:
\[ r = \frac{C}{2\pi} = \frac{176}{2\pi} \]
\[ r = \frac{88}{\pi} \]
Step 2: Determine the Side of the Square
- According to the problem, the radius of the circle is equal to the side of the square (s):
\[ s = r = \frac{88}{\pi} \]
Step 3: Find the Length of the Rectangle
- The length (L) of the rectangle is \( \frac{4}{7} \) of the side of the square:
\[ L = \frac{4}{7}s = \frac{4}{7} \times \frac{88}{\pi} \]
\[ L = \frac{352}{7\pi} \]
Step 4: Calculate the Area of the Rectangle
- The area (A) of the rectangle is given by:
\[ A = L \times \text{breadth} \]
- The breadth of the rectangle is provided as 12 cm:
\[ A = \left(\frac{352}{7\pi}\right) \times 12 \]
\[ A = \frac{4224}{7\pi} \]
Step 5: Approximate the Area
- Using \( \pi \approx 3.14 \):
\[ A \approx \frac{4224}{21.98} \approx 192 \text{ cm}^2 \]
Thus, the area of the rectangle is 192 cm². The correct answer is option 'E'.
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The length of a rectangle is 4/7 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 176 cm. What is the area of the rectangle if the breadth of the rectangle is 12 cm ?a)326 cm2b)352 cm2c)288 cm2d)336 cm2e)192 cm2Correct answer is option 'E'. Can you explain this answer?
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The length of a rectangle is 4/7 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 176 cm. What is the area of the rectangle if the breadth of the rectangle is 12 cm ?a)326 cm2b)352 cm2c)288 cm2d)336 cm2e)192 cm2Correct answer is option 'E'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about The length of a rectangle is 4/7 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 176 cm. What is the area of the rectangle if the breadth of the rectangle is 12 cm ?a)326 cm2b)352 cm2c)288 cm2d)336 cm2e)192 cm2Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of a rectangle is 4/7 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 176 cm. What is the area of the rectangle if the breadth of the rectangle is 12 cm ?a)326 cm2b)352 cm2c)288 cm2d)336 cm2e)192 cm2Correct answer is option 'E'. Can you explain this answer?.
The length of a rectangle is 4/7 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 176 cm. What is the area of the rectangle if the breadth of the rectangle is 12 cm ?a)326 cm2b)352 cm2c)288 cm2d)336 cm2e)192 cm2Correct answer is option 'E'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about The length of a rectangle is 4/7 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 176 cm. What is the area of the rectangle if the breadth of the rectangle is 12 cm ?a)326 cm2b)352 cm2c)288 cm2d)336 cm2e)192 cm2Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of a rectangle is 4/7 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 176 cm. What is the area of the rectangle if the breadth of the rectangle is 12 cm ?a)326 cm2b)352 cm2c)288 cm2d)336 cm2e)192 cm2Correct answer is option 'E'. Can you explain this answer?.
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