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The area of a rectangular field is 2000 sq.m and its 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
- a)(205m, 80m)
- b)(50m, 40)
- c)(40m, 50m)
- d)none
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The area of a rectangular field is 2000 sq.m and its perimeter is 180m...
Solution:
Given, area of rectangular field = 2000 sq.m
Perimeter of rectangular field = 180 m
Let the length of the rectangular field be x m
Then, breadth of the rectangular field = 2000/x m
Perimeter of rectangular field = 2(length + breadth)
=> 180 = 2(x + 2000/x)
=> x^2 - 90x + 2000 = 0 ... (dividing by 2)
This is a quadratic equation in x which can be solved using the quadratic formula.
x = [90 ± sqrt(90^2 - 4*2000)]/2
x = [90 ± 10]/2
x = 50 or x = 40
If x = 50, then breadth = 2000/50 = 40
If x = 40, then breadth = 2000/40 = 50
Therefore, the length and breadth of the rectangular field are 50m and 40m respectively.
Hence, option B is the correct answer.
Given, area of rectangular field = 2000 sq.m
Perimeter of rectangular field = 180 m
Let the length of the rectangular field be x m
Then, breadth of the rectangular field = 2000/x m
Perimeter of rectangular field = 2(length + breadth)
=> 180 = 2(x + 2000/x)
=> x^2 - 90x + 2000 = 0 ... (dividing by 2)
This is a quadratic equation in x which can be solved using the quadratic formula.
x = [90 ± sqrt(90^2 - 4*2000)]/2
x = [90 ± 10]/2
x = 50 or x = 40
If x = 50, then breadth = 2000/50 = 40
If x = 40, then breadth = 2000/40 = 50
Therefore, the length and breadth of the rectangular field are 50m and 40m respectively.
Hence, option B is the correct answer.
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Community Answer
The area of a rectangular field is 2000 sq.m and its perimeter is 180m...
Area of rectangle=lb=2000
Perimeter of rectangle=2(l+b)=180
Therefore
2(l+b) =180
l+b=90
b=90-l
substitute in lb=2000
we get equation of
l(90-l) =2000
90l-l^2=2000
l^2-90l+2000=0
After solving the equation we get roots as 50 and 40
Perimeter of rectangle=2(l+b)=180
Therefore
2(l+b) =180
l+b=90
b=90-l
substitute in lb=2000
we get equation of
l(90-l) =2000
90l-l^2=2000
l^2-90l+2000=0
After solving the equation we get roots as 50 and 40
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