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The area of a rectangular field is to 1000 square metre and its perimeter is 180 m form a quadratic equation by taking the length of a fail does X and salt to find the length and breadth of the field the length and breadth are?
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The area of a rectangular field is to 1000 square metre and its perime...
Given:
- Area of the rectangular field = 1000 sq m
- Perimeter of the rectangular field = 180 m
Let:
- Length of the field = X m
- Breadth of the field = Y m
Formulating the equation:
- Area of a rectangle = Length * Breadth
- Perimeter of a rectangle = 2(Length + Breadth)
Given that the area of the rectangle is 1000 sq m, we have:
X * Y = 1000 (equation 1)
Given that the perimeter of the rectangle is 180 m, we have:
2(X + Y) = 180
X + Y = 90 (equation 2)
Solving the equations:
From equation 2, we have X + Y = 90
We can rewrite this as: Y = 90 - X
Substitute Y = 90 - X into equation 1:
X * (90 - X) = 1000
90X - X^2 = 1000
X^2 - 90X + 1000 = 0
This is a quadratic equation that can be factored as:
(X - 40)(X - 50) = 0
So, X = 40 or X = 50
Finding the length and breadth:
If X = 40, then Y = 90 - 40 = 50
If X = 50, then Y = 90 - 50 = 40
Therefore, the length and breadth of the rectangular field are:
Length = 40 m, Breadth = 50 m
- Area of the rectangular field = 1000 sq m
- Perimeter of the rectangular field = 180 m
Let:
- Length of the field = X m
- Breadth of the field = Y m
Formulating the equation:
- Area of a rectangle = Length * Breadth
- Perimeter of a rectangle = 2(Length + Breadth)
Given that the area of the rectangle is 1000 sq m, we have:
X * Y = 1000 (equation 1)
Given that the perimeter of the rectangle is 180 m, we have:
2(X + Y) = 180
X + Y = 90 (equation 2)
Solving the equations:
From equation 2, we have X + Y = 90
We can rewrite this as: Y = 90 - X
Substitute Y = 90 - X into equation 1:
X * (90 - X) = 1000
90X - X^2 = 1000
X^2 - 90X + 1000 = 0
This is a quadratic equation that can be factored as:
(X - 40)(X - 50) = 0
So, X = 40 or X = 50
Finding the length and breadth:
If X = 40, then Y = 90 - 40 = 50
If X = 50, then Y = 90 - 50 = 40
Therefore, the length and breadth of the rectangular field are:
Length = 40 m, Breadth = 50 m
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The area of a rectangular field is to 1000 square metre and its perimeter is 180 m form a quadratic equation by taking the length of a fail does X and salt to find the length and breadth of the field the length and breadth are?
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The area of a rectangular field is to 1000 square metre and its perimeter is 180 m form a quadratic equation by taking the length of a fail does X and salt to find the length and breadth of the field the length and breadth are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The area of a rectangular field is to 1000 square metre and its perimeter is 180 m form a quadratic equation by taking the length of a fail does X and salt to find the length and breadth of the field the length and breadth are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a rectangular field is to 1000 square metre and its perimeter is 180 m form a quadratic equation by taking the length of a fail does X and salt to find the length and breadth of the field the length and breadth are?.
The area of a rectangular field is to 1000 square metre and its perimeter is 180 m form a quadratic equation by taking the length of a fail does X and salt to find the length and breadth of the field the length and breadth are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The area of a rectangular field is to 1000 square metre and its perimeter is 180 m form a quadratic equation by taking the length of a fail does X and salt to find the length and breadth of the field the length and breadth are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a rectangular field is to 1000 square metre and its perimeter is 180 m form a quadratic equation by taking the length of a fail does X and salt to find the length and breadth of the field the length and breadth are?.
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