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A man takes 6 km. distance to go around the rectangular area. If the area of the rectangle is 2 sq. km., find the difference between length, and breadth.
- a)2 km.
- b)0.5 km.
- c)1 km
- d)0.75 km
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A man takes 6 km. distance to go around the rectangular area. If the a...
To solve this problem, let's assume the length of the rectangle as 'l' and the breadth as 'b'.
Given that the perimeter of the rectangle is 6 km, we can write the equation as:
2(l + b) = 6
Simplifying the equation, we have:
l + b = 3
Now, we are given that the area of the rectangle is 2 sq. km. The formula for the area of a rectangle is:
Area = length × breadth
Substituting the given values, we get:
2 = l × b
Now, we have two equations:
l + b = 3
l × b = 2
We can solve this system of equations to find the values of 'l' and 'b'.
To find the difference between the length and breadth, we can subtract the smaller value from the larger value. Let's assume that 'l' is the larger value.
l = 3 - b
Substituting this value in the second equation:
(3 - b) × b = 2
Expanding and rearranging the equation, we get:
b^2 - 3b + 2 = 0
Factoring the equation, we have:
(b - 1)(b - 2) = 0
So, the possible values for 'b' are 1 and 2.
Case 1: b = 1
Substituting this value in the equation l + b = 3, we get:
l + 1 = 3
l = 2
Case 2: b = 2
Substituting this value in the equation l + b = 3, we get:
l + 2 = 3
l = 1
Therefore, the possible values for the length and breadth are:
Length (l) = 2 km, Breadth (b) = 1 km
or
Length (l) = 1 km, Breadth (b) = 2 km
In both cases, the difference between the length and breadth is 1 km. Hence, the correct answer is option C) 1 km.
Given that the perimeter of the rectangle is 6 km, we can write the equation as:
2(l + b) = 6
Simplifying the equation, we have:
l + b = 3
Now, we are given that the area of the rectangle is 2 sq. km. The formula for the area of a rectangle is:
Area = length × breadth
Substituting the given values, we get:
2 = l × b
Now, we have two equations:
l + b = 3
l × b = 2
We can solve this system of equations to find the values of 'l' and 'b'.
To find the difference between the length and breadth, we can subtract the smaller value from the larger value. Let's assume that 'l' is the larger value.
l = 3 - b
Substituting this value in the second equation:
(3 - b) × b = 2
Expanding and rearranging the equation, we get:
b^2 - 3b + 2 = 0
Factoring the equation, we have:
(b - 1)(b - 2) = 0
So, the possible values for 'b' are 1 and 2.
Case 1: b = 1
Substituting this value in the equation l + b = 3, we get:
l + 1 = 3
l = 2
Case 2: b = 2
Substituting this value in the equation l + b = 3, we get:
l + 2 = 3
l = 1
Therefore, the possible values for the length and breadth are:
Length (l) = 2 km, Breadth (b) = 1 km
or
Length (l) = 1 km, Breadth (b) = 2 km
In both cases, the difference between the length and breadth is 1 km. Hence, the correct answer is option C) 1 km.
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Community Answer
A man takes 6 km. distance to go around the rectangular area. If the a...
Calculations:
Perimeter of rectangular area = 2(Lenght + Breadth) = 6 km ........(1)
⇒ (Lenght + Breadth) = 3 km
Then,
Area of rectangular area = Lenght × Breadth = 2 sq Km
⇒ Length × Breadth = 2
⇒ Length = 2/ Breadth
Putting in equation (1),
⇒ {2/ Breadth) + Breadth} = 3 km
⇒ Breadth = 2 , 1
⇒ Length = 1, 2.
Since Length is greater than breadth, so
Length = 2 Km and Breadth = 1 Km
Here, the difference between length & breadth is = 2 - 1 = 1 km
Hence, the correct answer is "1 Km".
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A man takes 6 km. distance to go around the rectangular area. If the area of the rectangle is 2 sq. km., find the difference between length, and breadth.a) 2 km.b)0.5 km.c)1 kmd) 0.75 kmCorrect answer is option 'C'. Can you explain this answer?
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