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The length of a rectangle exceeds its breadth by 9 CM if the length and breadth 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 the given rectangle?
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The length of a rectangle exceeds its breadth by 9 CM if the length an...
To find the length and breadth of the given rectangle, we will use algebra. Let's denote the breadth of the rectangle as **b** cm, and the length as **l** cm. The problem states the following:
1. Establishing the relationship between length and breadth
- Length exceeds breadth by 9 cm:
- \( l = b + 9 \)
2. Area of the original rectangle
- The area \( A \) of the original rectangle is:
- \( A = l \times b \)
- Substituting for \( l \):
- \( A = (b + 9) \times b \)
- \( A = b^2 + 9b \)
3. Area of the new rectangle
- If both dimensions are increased by 3 cm:
- New length \( = l + 3 = b + 12 \)
- New breadth \( = b + 3 \)
- The area \( A' \) of the new rectangle is:
- \( A' = (b + 12) \times (b + 3) \)
- \( A' = b^2 + 15b + 36 \)
4. Relating the areas
- The area of the new rectangle is 84 cm² more than the original rectangle:
- \( A' = A + 84 \)
- \( b^2 + 15b + 36 = b^2 + 9b + 84 \)
5. Simplifying the equation
- Cancel \( b^2 \) from both sides:
- \( 15b + 36 = 9b + 84 \)
- Rearranging gives:
- \( 6b = 48 \)
- \( b = 8 \)
6. Finding the length
- Now, substitute \( b \) back to find \( l \):
- \( l = b + 9 = 8 + 9 = 17 \)
Conclusion
- The dimensions of the rectangle are:
- **Length = 17 cm**
- **Breadth = 8 cm**
1. Establishing the relationship between length and breadth
- Length exceeds breadth by 9 cm:
- \( l = b + 9 \)
2. Area of the original rectangle
- The area \( A \) of the original rectangle is:
- \( A = l \times b \)
- Substituting for \( l \):
- \( A = (b + 9) \times b \)
- \( A = b^2 + 9b \)
3. Area of the new rectangle
- If both dimensions are increased by 3 cm:
- New length \( = l + 3 = b + 12 \)
- New breadth \( = b + 3 \)
- The area \( A' \) of the new rectangle is:
- \( A' = (b + 12) \times (b + 3) \)
- \( A' = b^2 + 15b + 36 \)
4. Relating the areas
- The area of the new rectangle is 84 cm² more than the original rectangle:
- \( A' = A + 84 \)
- \( b^2 + 15b + 36 = b^2 + 9b + 84 \)
5. Simplifying the equation
- Cancel \( b^2 \) from both sides:
- \( 15b + 36 = 9b + 84 \)
- Rearranging gives:
- \( 6b = 48 \)
- \( b = 8 \)
6. Finding the length
- Now, substitute \( b \) back to find \( l \):
- \( l = b + 9 = 8 + 9 = 17 \)
Conclusion
- The dimensions of the rectangle are:
- **Length = 17 cm**
- **Breadth = 8 cm**
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The length of a rectangle exceeds its breadth by 9 CM if the length and breadth 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 the given rectangle?
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The length of a rectangle exceeds its breadth by 9 CM if the length and breadth 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 the given rectangle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The length of a rectangle exceeds its breadth by 9 CM if the length and breadth 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 the given rectangle? covers all topics & solutions for UPSC 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 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 the given rectangle?.
The length of a rectangle exceeds its breadth by 9 CM if the length and breadth 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 the given rectangle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The length of a rectangle exceeds its breadth by 9 CM if the length and breadth 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 the given rectangle? covers all topics & solutions for UPSC 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 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 the given rectangle?.
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