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In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 4m their ratio becomes 10:7. The area of the original rectangle in m² is?
- a)384
- b)486
- c)546
- d)864
- e)None of the Above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a rectangle the ratio of the length and breadth is 3:2. If each of ...
[3x + 4 / 2x + 4] = 10/ 7
x = 12
Area of the original rectangle = 3x * 2x = 6x²
Area of the original rectangle = 6 * 144 = 864 m²
x = 12
Area of the original rectangle = 3x * 2x = 6x²
Area of the original rectangle = 6 * 144 = 864 m²
Most Upvoted Answer
In a rectangle the ratio of the length and breadth is 3:2. If each of ...
Understanding the Problem
To find the area of the original rectangle, we start by acknowledging the given ratios and conditions.
Step 1: Define Variables
- Let the length of the rectangle be 3x and the breadth be 2x, based on the ratio of 3:2.
Step 2: Set Up the Equation
- According to the problem, when both length and breadth are increased by 4m, the new ratio becomes 10:7.
- This can be expressed as:
(3x + 4) / (2x + 4) = 10 / 7
Step 3: Cross-Multiply and Simplify
- Cross-multiplying gives:
7(3x + 4) = 10(2x + 4)
- Expanding both sides results in:
21x + 28 = 20x + 40
Step 4: Solve for x
- Rearranging yields:
21x - 20x = 40 - 28
x = 12
Step 5: Calculate Length and Breadth
- Plugging x back into our expressions:
Length = 3x = 36m
Breadth = 2x = 24m
Step 6: Find the Area
- The area of the rectangle is calculated as:
Area = Length × Breadth = 36m × 24m = 864m²
Conclusion
The area of the original rectangle is 864m², confirming that the correct answer is option 'D'.
To find the area of the original rectangle, we start by acknowledging the given ratios and conditions.
Step 1: Define Variables
- Let the length of the rectangle be 3x and the breadth be 2x, based on the ratio of 3:2.
Step 2: Set Up the Equation
- According to the problem, when both length and breadth are increased by 4m, the new ratio becomes 10:7.
- This can be expressed as:
(3x + 4) / (2x + 4) = 10 / 7
Step 3: Cross-Multiply and Simplify
- Cross-multiplying gives:
7(3x + 4) = 10(2x + 4)
- Expanding both sides results in:
21x + 28 = 20x + 40
Step 4: Solve for x
- Rearranging yields:
21x - 20x = 40 - 28
x = 12
Step 5: Calculate Length and Breadth
- Plugging x back into our expressions:
Length = 3x = 36m
Breadth = 2x = 24m
Step 6: Find the Area
- The area of the rectangle is calculated as:
Area = Length × Breadth = 36m × 24m = 864m²
Conclusion
The area of the original rectangle is 864m², confirming that the correct answer is option 'D'.
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In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 4m their ratio becomes 10:7. The area of the original rectangle in m² is?a)384b)486c)546d)864e)None of the AboveCorrect answer is option 'D'. Can you explain this answer?
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