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The area of a rectangular field is 2000 sq. m and it's perimeter is 180m . Form a quadratic equation by taking the length of the field as x and solve it 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 2000 sq. m and it's perimeter is 18...
Given Information
- Area of the rectangular field = 2000 sq. m
- Perimeter of the rectangular field = 180 m
Forming Equations
Let the length of the field be x meters. Then, the breadth can be expressed as:
- Breadth = (Area / Length) = 2000 / x
Using the perimeter formula:
- Perimeter = 2(Length + Breadth) = 180
Substituting the breadth in the perimeter equation:
- 2(x + (2000 / x)) = 180
Rearranging the Equation
Multiply both sides by 1/2:
- x + (2000 / x) = 90
Now, multiply through by x to eliminate the fraction:
- x^2 + 2000 = 90x
Rearranging gives the quadratic equation:
- x^2 - 90x + 2000 = 0
Solving the Quadratic Equation
We can apply the quadratic formula, where a = 1, b = -90, and c = 2000:
- Discriminant = b^2 - 4ac = (-90)^2 - 4(1)(2000) = 8100 - 8000 = 100
The roots are:
- x = [90 ± √100] / 2
Calculating the roots:
- x = (90 ± 10) / 2
This gives:
- x = 50 or x = 40
Finding Length and Breadth
1. If Length (x) = 50 m, then:
- Breadth = 2000 / 50 = 40 m
2. If Length (x) = 40 m, then:
- Breadth = 2000 / 40 = 50 m
Final Dimensions
- Length = 50 m, Breadth = 40 m (or vice versa)
Thus, the dimensions of the rectangular field are 50 meters and 40 meters.
- Area of the rectangular field = 2000 sq. m
- Perimeter of the rectangular field = 180 m
Forming Equations
Let the length of the field be x meters. Then, the breadth can be expressed as:
- Breadth = (Area / Length) = 2000 / x
Using the perimeter formula:
- Perimeter = 2(Length + Breadth) = 180
Substituting the breadth in the perimeter equation:
- 2(x + (2000 / x)) = 180
Rearranging the Equation
Multiply both sides by 1/2:
- x + (2000 / x) = 90
Now, multiply through by x to eliminate the fraction:
- x^2 + 2000 = 90x
Rearranging gives the quadratic equation:
- x^2 - 90x + 2000 = 0
Solving the Quadratic Equation
We can apply the quadratic formula, where a = 1, b = -90, and c = 2000:
- Discriminant = b^2 - 4ac = (-90)^2 - 4(1)(2000) = 8100 - 8000 = 100
The roots are:
- x = [90 ± √100] / 2
Calculating the roots:
- x = (90 ± 10) / 2
This gives:
- x = 50 or x = 40
Finding Length and Breadth
1. If Length (x) = 50 m, then:
- Breadth = 2000 / 50 = 40 m
2. If Length (x) = 40 m, then:
- Breadth = 2000 / 40 = 50 m
Final Dimensions
- Length = 50 m, Breadth = 40 m (or vice versa)
Thus, the dimensions of the rectangular field are 50 meters and 40 meters.
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The area of a rectangular field is 2000 sq. m and it's perimeter is 180m . Form a quadratic equation by taking the length of the field as x and solve it 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 2000 sq. m and it's perimeter is 180m . Form a quadratic equation by taking the length of the field as x and solve it to find the length and breadth of the field. The length and breadth are? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The area of a rectangular field is 2000 sq. m and it's perimeter is 180m . Form a quadratic equation by taking the length of the field as x and solve it to find the length and breadth of the field. The length and breadth are? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a rectangular field is 2000 sq. m and it's perimeter is 180m . Form a quadratic equation by taking the length of the field as x and solve it to find the length and breadth of the field. The length and breadth are?.
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