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The ratio of the radius of a circle and length of a rectangular field is 2 : 7. If the perimeter of circle and that of the rectangular field be 176 m and 322 m respectively, what is the width of the rectangular field?
- a)85 m
- b)63 m
- c)58 m
- d)77 m
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Understanding the Problem
To find the width of the rectangular field, we first need to analyze the given information regarding the circle and the rectangle.
Given Ratios and Perimeters
- Ratio of the radius of the circle (r) to the length of the rectangle (l) = 2:7
- Perimeter of the circle = 176 m
- Perimeter of the rectangular field = 322 m
Calculating the Radius of the Circle
- The formula for the perimeter (circumference) of a circle is 2 * π * r.
- Setting it equal to 176 m:
2 * π * r = 176
r = 176 / (2 * π)
r ≈ 28 m (using π ≈ 3.14)
Finding the Length of the Rectangle
- Using the ratio 2:7, we can express the length (l) in terms of the radius (r):
l = (7/2) * r
l = (7/2) * 28 = 98 m
Calculating the Width of the Rectangle
- The perimeter (P) of a rectangle is given by the formula:
P = 2 * (length + width)
- For the rectangular field with a perimeter of 322 m:
322 = 2 * (98 + width)
161 = 98 + width
width = 161 - 98
width = 63 m
Conclusion
The width of the rectangular field is 63 m, which corresponds to option 'B'.
To find the width of the rectangular field, we first need to analyze the given information regarding the circle and the rectangle.
Given Ratios and Perimeters
- Ratio of the radius of the circle (r) to the length of the rectangle (l) = 2:7
- Perimeter of the circle = 176 m
- Perimeter of the rectangular field = 322 m
Calculating the Radius of the Circle
- The formula for the perimeter (circumference) of a circle is 2 * π * r.
- Setting it equal to 176 m:
2 * π * r = 176
r = 176 / (2 * π)
r ≈ 28 m (using π ≈ 3.14)
Finding the Length of the Rectangle
- Using the ratio 2:7, we can express the length (l) in terms of the radius (r):
l = (7/2) * r
l = (7/2) * 28 = 98 m
Calculating the Width of the Rectangle
- The perimeter (P) of a rectangle is given by the formula:
P = 2 * (length + width)
- For the rectangular field with a perimeter of 322 m:
322 = 2 * (98 + width)
161 = 98 + width
width = 161 - 98
width = 63 m
Conclusion
The width of the rectangular field is 63 m, which corresponds to option 'B'.
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