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The area of a rectangle is (x²-11x+28)sq units. if the breadth of the rectangle is (x -7) units then find its length.?
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The area of a rectangle is (x²-11x+28)sq units. if the breadth of the ...
Understanding the Problem
To find the length of the rectangle, we start with the area formula:
- Area = Length × Breadth
Given:
- Area = x² - 11x + 28
- Breadth = x - 7
Finding Length
We can express the length (L) in terms of the area and breadth:
- L = Area / Breadth
Substituting the provided values:
- L = (x² - 11x + 28) / (x - 7)
Simplifying the Expression
To simplify, we perform polynomial long division or factoring:
1. Factoring the Area:
- The quadratic expression x² - 11x + 28 can be factored as (x - 4)(x - 7).
2. Substituting into the Length Formula:
- L = [(x - 4)(x - 7)] / (x - 7)
3. Cancelling Common Factors:
- If x ≠ 7, we can cancel (x - 7):
- L = x - 4
Conclusion
The length of the rectangle is:
- Length = x - 4 (for x ≠ 7)
This means that for any value of x other than 7, the length can be calculated directly using this formula. Remember to always check the conditions under which the expressions are valid.
To find the length of the rectangle, we start with the area formula:
- Area = Length × Breadth
Given:
- Area = x² - 11x + 28
- Breadth = x - 7
Finding Length
We can express the length (L) in terms of the area and breadth:
- L = Area / Breadth
Substituting the provided values:
- L = (x² - 11x + 28) / (x - 7)
Simplifying the Expression
To simplify, we perform polynomial long division or factoring:
1. Factoring the Area:
- The quadratic expression x² - 11x + 28 can be factored as (x - 4)(x - 7).
2. Substituting into the Length Formula:
- L = [(x - 4)(x - 7)] / (x - 7)
3. Cancelling Common Factors:
- If x ≠ 7, we can cancel (x - 7):
- L = x - 4
Conclusion
The length of the rectangle is:
- Length = x - 4 (for x ≠ 7)
This means that for any value of x other than 7, the length can be calculated directly using this formula. Remember to always check the conditions under which the expressions are valid.
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The area of a rectangle is (x²-11x+28)sq units. if the breadth of the rectangle is (x -7) units then find its length.?
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The area of a rectangle is (x²-11x+28)sq units. if the breadth of the rectangle is (x -7) units then find its length.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The area of a rectangle is (x²-11x+28)sq units. if the breadth of the rectangle is (x -7) units then find its length.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a rectangle is (x²-11x+28)sq units. if the breadth of the rectangle is (x -7) units then find its length.?.
The area of a rectangle is (x²-11x+28)sq units. if the breadth of the rectangle is (x -7) units then find its length.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The area of a rectangle is (x²-11x+28)sq units. if the breadth of the rectangle is (x -7) units then find its length.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a rectangle is (x²-11x+28)sq units. if the breadth of the rectangle is (x -7) units then find its length.?.
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