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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, 40m)
c)(40m, 50m)
d)none
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The area of a rectangular field is 2000 sq.m and itsperimeter is 180m....
Let the length be l and the breadth be b. now area = 2000 sq.m so length * breadth = 2000; l*b=2000.
now perimeter = 180m
so 2 ( l + b ) =180;
l + b = 90;
l = 90 - b.
substituting this value of l in l * b = 2000,
( 90 - b ) * b = 2000;
90b - b^2 = 2000;
b^2 - 90b + 2000 = 0;
b^2 - 40b - 50b - 2000 = 0;
b ( b - 40 ) - 50( b - 40 ) = 0;
( b - 40 )( b - 50 ) = 0;
b = 40 or b = 50;
so l = 40 or l = 50 but the longer side is considered the length and the shorter one the breadth.
so length = 50 m and breadth = 40 m
Most Upvoted Answer
The area of a rectangular field is 2000 sq.m and itsperimeter is 180m....
Given:
Area of rectangular field = 2000 sq.m
Perimeter of rectangular field = 180m
To find:
Length and Breadth of the field
Solution:
Let's assume that Length of the rectangular field is 'x' meters and Breadth is 'y' meters.
We know the area of the rectangle is given by:
Area = Length * Breadth
Substituting the given values, we get:
2000 = x * y ---(1)
Also, we know that the perimeter of the rectangle is given by:
Perimeter = 2 * (Length + Breadth)
Substituting the given values, we get:
180 = 2 * (x + y)
Simplifying, we get:
x + y = 90 ---(2)
We have two equations (1) and (2) and two variables (x and y). We can solve these equations simultaneously to find the values of x and y.
Let's solve equation (2) for y:
y = 90 - x ---(3)
Substituting equation (3) in equation (1), we get:
2000 = x * (90 - x)
Simplifying, we get:
2000 = 90x - x^2
Rearranging, we get:
x^2 - 90x + 2000 = 0
This is a quadratic equation in x. We can solve this equation using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
where a = 1, b = -90, and c = 2000
Substituting the values, we get:
x = [90 ± sqrt(90^2 - 4*1*2000)] / 2*1
Simplifying, we get:
x = [90 ± sqrt(8100 - 8000)] / 2
x = [90 ± 10] / 2
x = 50 or x = 40
Now, we can use equation (3) to find the corresponding values of y:
For x = 50, y = 90 - 50 = 40
For x = 40, y = 90 - 40 = 50
Therefore, the length and breadth of the rectangular field are 50m and 40m respectively.
Hence, the correct option is (b).
Area of rectangular field = 2000 sq.m
Perimeter of rectangular field = 180m
To find:
Length and Breadth of the field
Solution:
Let's assume that Length of the rectangular field is 'x' meters and Breadth is 'y' meters.
We know the area of the rectangle is given by:
Area = Length * Breadth
Substituting the given values, we get:
2000 = x * y ---(1)
Also, we know that the perimeter of the rectangle is given by:
Perimeter = 2 * (Length + Breadth)
Substituting the given values, we get:
180 = 2 * (x + y)
Simplifying, we get:
x + y = 90 ---(2)
We have two equations (1) and (2) and two variables (x and y). We can solve these equations simultaneously to find the values of x and y.
Let's solve equation (2) for y:
y = 90 - x ---(3)
Substituting equation (3) in equation (1), we get:
2000 = x * (90 - x)
Simplifying, we get:
2000 = 90x - x^2
Rearranging, we get:
x^2 - 90x + 2000 = 0
This is a quadratic equation in x. We can solve this equation using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
where a = 1, b = -90, and c = 2000
Substituting the values, we get:
x = [90 ± sqrt(90^2 - 4*1*2000)] / 2*1
Simplifying, we get:
x = [90 ± sqrt(8100 - 8000)] / 2
x = [90 ± 10] / 2
x = 50 or x = 40
Now, we can use equation (3) to find the corresponding values of y:
For x = 50, y = 90 - 50 = 40
For x = 40, y = 90 - 40 = 50
Therefore, the length and breadth of the rectangular field are 50m and 40m respectively.
Hence, the correct option is (b).
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Community Answer
The area of a rectangular field is 2000 sq.m and itsperimeter is 180m....
Area of rectangle = l × b = 2000.
Perimeter of rectangle = 2 (l+b)=180.
L+b =90.... L = 90 -b.
(90-b) × b = 2000.
90b-b²=2000.
b² - 90b +2000=0.
b² - 40b - 50b +2000=0.
b(b-40) - 50(b-40)=0.
(b-40)(b-50)=0.
Hence length and breadth is 50 and 40.
Correct option will be (b)
Option (c) is wrong because in a rectangle long side is considered as length and small side as breadth
Perimeter of rectangle = 2 (l+b)=180.
L+b =90.... L = 90 -b.
(90-b) × b = 2000.
90b-b²=2000.
b² - 90b +2000=0.
b² - 40b - 50b +2000=0.
b(b-40) - 50(b-40)=0.
(b-40)(b-50)=0.
Hence length and breadth is 50 and 40.
Correct option will be (b)
Option (c) is wrong because in a rectangle long side is considered as length and small side as breadth
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