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The perimeter of a rectangle is 300m. If the difference between the length and breadth of the rectangle is 10m, then what is the circumference of the largest circle that can be drawn inside the rectangle?
  • a)
    220m
  • b)
    110m
  • c)
    140m
  • d)
    120m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The perimeter of a rectangle is 300m. If the difference between the le...
Perimeter = 2(l + b)
2(l + b) = 300 (l + b) = 150m
Now, b + 10 + b = 150
2b = 140
b = 70m
The largest circle drawn inside the rectangle will have diameter equal to the breadth of the rectangle.
Circumference of the circle = 22/7 × d
= 22/7 × 70
= 220 m
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Most Upvoted Answer
The perimeter of a rectangle is 300m. If the difference between the le...
Given Information
- The perimeter of the rectangle = 300m
- The difference between length (L) and breadth (B) = 10m
Formulating Equations
1. The formula for the perimeter (P) of a rectangle is given by:
- P = 2(L + B)
- Therefore, 2(L + B) = 300
- Simplifying gives: L + B = 150
2. According to the difference condition:
- L - B = 10
Solving the Equations
- We have two equations:
- L + B = 150 (1)
- L - B = 10 (2)
- Adding equations (1) and (2):
- (L + B) + (L - B) = 150 + 10
- 2L = 160
- L = 80m
- Substituting L back into equation (1):
- 80 + B = 150
- B = 150 - 80 = 70m
Finding the Radius of the Circle
- The largest circle that can be inscribed in the rectangle will have a diameter equal to the smaller dimension (breadth):
- Diameter = B = 70m
- Radius (r) = Diameter / 2 = 70 / 2 = 35m
Calculating Circumference
- The formula for the circumference (C) of a circle is:
- C = 2πr
- C = 2 * π * 35
- Approximating π as 3.14:
- C ≈ 2 * 3.14 * 35 = 220m
Final Answer
- The circumference of the largest circle that can be drawn inside the rectangle is 220m (Option A).
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The perimeter of a rectangle is 300m. If the difference between the length and breadth of the rectangle is 10m, then what is the circumference of the largest circle that can be drawn inside the rectangle?a)220mb)110mc)140md)120mCorrect answer is option 'A'. Can you explain this answer?
Question Description
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