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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 area of the rectangle?
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If in a rectangle the length is increased and breadth is reduced each ...
To solve the problem, let's define the variables and set up the equations based on the given conditions.
Step 1: Define Variables
- Let the length of the rectangle be L.
- Let the breadth of the rectangle be B.
Step 2: Set Up the Equations
1. First Condition:
- When length is increased by 2 and breadth is decreased by 2:
- New Length = L + 2
- New Breadth = B - 2
- Area Reduction:
- \[(L + 2)(B - 2) = LB - 28\]
Expanding the left side:
- LB - 2L + 2B - 4 = LB - 28
- Simplifying gives:
- -2L + 2B - 4 = -28
- Therefore,
- 2B - 2L = -24
- Dividing by 2:
- B - L = -12
- Hence,
- B = L - 12 (Equation 1)
2. Second Condition:
- When length is reduced by 1 and breadth is increased by 2:
- New Length = L - 1
- New Breadth = B + 2
- Area Increase:
- \[(L - 1)(B + 2) = LB + 33\]
Expanding the left side:
- LB + 2L - B - 2 = LB + 33
- Simplifying gives:
- 2L - B - 2 = 33
- Therefore,
- 2L - B = 35
- (Equation 2)
Step 3: Solve the Equations
Using Equations 1 and 2:
- Substitute Equation 1 into Equation 2:
- 2L - (L - 12) = 35
- This simplifies to:
- L + 12 = 35
- Hence,
- L = 23
Using L = 23 in Equation 1:
- B = 23 - 12 = 11
Step 4: Find the Area
- Area \(A = L \times B = 23 \times 11 = 253 \text{ square units}\)
Conclusion
The area of the rectangle is 253 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 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 area of the rectangle? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 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 area of the rectangle? covers all topics & solutions for Class 10 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 area of the rectangle?.
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