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If in a rectangle the length is increased and breadth is reduced each by two units the area gets reduced by 28 square units if however the length is reduced by one and the breadth is increased by 2 units the area increases by 33 square units find the total area of the rectangle?
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If in a rectangle the length is increased and breadth is reduced each ...
Problem Statement
In this problem, we have a rectangle with a length (L) and breadth (B). We need to analyze the changes in area based on different modifications to these dimensions.
Step 1: Setting Up Equations
- Original Area: A = L * B
- First Scenario:
- Length increased by 2: L + 2
- Breadth reduced by 2: B - 2
- New Area: (L + 2)(B - 2)
- Area reduction: A - 28 = (L + 2)(B - 2)
- Expanding:
L * B - 28 = LB - 2L + 2B - 4
Therefore,
28 = 2L - 2B + 4
Which simplifies to:
2L - 2B = 24
Finally:
L - B = 12 (Equation 1)
- Second Scenario:
- Length reduced by 1: L - 1
- Breadth increased by 2: B + 2
- New Area: (L - 1)(B + 2)
- Area increase: A + 33 = (L - 1)(B + 2)
- Expanding:
L * B + 33 = LB + 2L - B - 2
Therefore,
33 = 2L - B - 2
Which simplifies to:
2L - B = 35 (Equation 2)
Step 2: Solving the Equations
- From Equation 1: L - B = 12
Thus, L = B + 12
- Substitute L in Equation 2:
2(B + 12) - B = 35
Which leads to:
B = 10
And substituting back:
L = 22
Step 3: Total Area Calculation
- Area = L * B = 22 * 10 = 220 square units.
Conclusion
The total area of the rectangle is 220 square units.
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If in a rectangle the length is increased and breadth is reduced each by two units the area gets reduced by 28 square units if however the length is reduced by one and the breadth is increased by 2 units the area increases by 33 square units find the total area of the rectangle?
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If in a rectangle the length is increased and breadth is reduced each by two units the area gets reduced by 28 square units if however the length is reduced by one and the breadth is increased by 2 units the area increases by 33 square units find the total area of the rectangle? for Interview Preparation 2024 is part of Interview Preparation preparation. The Question and answers have been prepared according to the Interview Preparation exam syllabus. Information about If in a rectangle the length is increased and breadth is reduced each by two units the area gets reduced by 28 square units if however the length is reduced by one and the breadth is increased by 2 units the area increases by 33 square units find the total area of the rectangle? covers all topics & solutions for Interview Preparation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in a rectangle the length is increased and breadth is reduced each by two units the area gets reduced by 28 square units if however the length is reduced by one and the breadth is increased by 2 units the area increases by 33 square units find the total area of the rectangle?.
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