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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.
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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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