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The area of a rectangle, 144 m long is the same as that of a square having a side 84 m long. The width of the rectangle is ?
- a)7 m
- b)14 m
- c)49 m
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The area of a rectangle, 144 m long is the same as that of a square ha...
Understanding the Problem
To find the width of the rectangle, we first need to understand the areas involved. We have a rectangle with a length of 144 m and a square with a side length of 84 m. The problem states that their areas are equal.
Calculating the Area of the Square
- The area of the square can be calculated as:
- Area = side × side
- Area = 84 m × 84 m = 7056 m²
Calculating the Area of the Rectangle
- The area of the rectangle is given by:
- Area = length × width
- Area = 144 m × width
Setting the Areas Equal
Since the areas are equal, we can set up the equation:
- 144 m × width = 7056 m²
Solving for Width
Now, let’s solve for the width:
- width = 7056 m² / 144 m
- width = 49 m
Conclusion
Thus, the width of the rectangle is 49 m. Therefore, the correct answer is option 'C'.
This problem illustrates how to equate areas of different shapes and solve for unknown dimensions, a common type of question in bank exams.
To find the width of the rectangle, we first need to understand the areas involved. We have a rectangle with a length of 144 m and a square with a side length of 84 m. The problem states that their areas are equal.
Calculating the Area of the Square
- The area of the square can be calculated as:
- Area = side × side
- Area = 84 m × 84 m = 7056 m²
Calculating the Area of the Rectangle
- The area of the rectangle is given by:
- Area = length × width
- Area = 144 m × width
Setting the Areas Equal
Since the areas are equal, we can set up the equation:
- 144 m × width = 7056 m²
Solving for Width
Now, let’s solve for the width:
- width = 7056 m² / 144 m
- width = 49 m
Conclusion
Thus, the width of the rectangle is 49 m. Therefore, the correct answer is option 'C'.
This problem illustrates how to equate areas of different shapes and solve for unknown dimensions, a common type of question in bank exams.
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Community Answer
The area of a rectangle, 144 m long is the same as that of a square ha...
Area of the square = (84 + 84) m2
Area of the rectangle = (144 x width) m2
Area of the rectangle = (144 x width) m2
From question both area would be same,
∴ Width = (84 x 84) / 144 m = 49 m
∴ Width = (84 x 84) / 144 m = 49 m
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