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The length of a rectangle exceeds its breadth by 9 CM if the length and breadth the are each increased by 3 cm the area of the new rectangle will be 84 CM square more than that of the given rectangle find the length and breadth of given rectangle.?
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The length of a rectangle exceeds its breadth by 9 CM if the length an...
Understanding the Problem
To find the length and breadth of the rectangle, we can define:
- Let the breadth be B cm.
- Then, the length L is B + 9 cm.
Setting Up the Equations
1. The area of the original rectangle:
- Area = Length × Breadth = (B + 9) × B
2. If both dimensions are increased by 3 cm:
- New Length = L + 3 = (B + 9) + 3 = B + 12 cm
- New Breadth = B + 3 cm
3. The area of the new rectangle:
- New Area = New Length × New Breadth = (B + 12) × (B + 3)
Creating the Equation
According to the problem, the new area is 84 cm² more than the original area:
- (B + 12)(B + 3) = (B + 9)B + 84
Expanding and Simplifying
1. Expand both sides:
- Left side: B² + 15B + 36
- Right side: B² + 9B + 84
2. Setting up the equation:
- B² + 15B + 36 = B² + 9B + 84
3. Simplifying gives:
- 6B - 48 = 0
4. So, B = 8 cm.
Finding Length
Now, substitute B back to find the length:
- L = B + 9 = 8 + 9 = 17 cm.
Final Dimensions
- Breadth (B): 8 cm
- Length (L): 17 cm
These dimensions satisfy the conditions of the problem!
To find the length and breadth of the rectangle, we can define:
- Let the breadth be B cm.
- Then, the length L is B + 9 cm.
Setting Up the Equations
1. The area of the original rectangle:
- Area = Length × Breadth = (B + 9) × B
2. If both dimensions are increased by 3 cm:
- New Length = L + 3 = (B + 9) + 3 = B + 12 cm
- New Breadth = B + 3 cm
3. The area of the new rectangle:
- New Area = New Length × New Breadth = (B + 12) × (B + 3)
Creating the Equation
According to the problem, the new area is 84 cm² more than the original area:
- (B + 12)(B + 3) = (B + 9)B + 84
Expanding and Simplifying
1. Expand both sides:
- Left side: B² + 15B + 36
- Right side: B² + 9B + 84
2. Setting up the equation:
- B² + 15B + 36 = B² + 9B + 84
3. Simplifying gives:
- 6B - 48 = 0
4. So, B = 8 cm.
Finding Length
Now, substitute B back to find the length:
- L = B + 9 = 8 + 9 = 17 cm.
Final Dimensions
- Breadth (B): 8 cm
- Length (L): 17 cm
These dimensions satisfy the conditions of the problem!
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The length of a rectangle exceeds its breadth by 9 CM if the length and breadth the are each increased by 3 cm the area of the new rectangle will be 84 CM square more than that of the given rectangle find the length and breadth of given rectangle.?
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The length of a rectangle exceeds its breadth by 9 CM if the length and breadth the are each increased by 3 cm the area of the new rectangle will be 84 CM square more than that of the given rectangle find the length and breadth of given rectangle.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The length of a rectangle exceeds its breadth by 9 CM if the length and breadth the are each increased by 3 cm the area of the new rectangle will be 84 CM square more than that of the given rectangle find the length and breadth of given rectangle.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of a rectangle exceeds its breadth by 9 CM if the length and breadth the are each increased by 3 cm the area of the new rectangle will be 84 CM square more than that of the given rectangle find the length and breadth of given rectangle.?.
The length of a rectangle exceeds its breadth by 9 CM if the length and breadth the are each increased by 3 cm the area of the new rectangle will be 84 CM square more than that of the given rectangle find the length and breadth of given rectangle.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The length of a rectangle exceeds its breadth by 9 CM if the length and breadth the are each increased by 3 cm the area of the new rectangle will be 84 CM square more than that of the given rectangle find the length and breadth of given rectangle.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of a rectangle exceeds its breadth by 9 CM if the length and breadth the are each increased by 3 cm the area of the new rectangle will be 84 CM square more than that of the given rectangle find the length and breadth of given rectangle.?.
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