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The perimeters of both, a square and a rectangle are each equal to 48 m and the difference between their areas is 4m2. The breadth of the rectangle is
- a)10 m
- b)12 m
- c)14 m
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The perimeters of both, a square and a rectangle are each equal to 48 ...
Let the length of rectangle = xm and its breadth = y m Also, let the side of the square be z m. Then,
2(x+y)=4z=48 ⇒ x+y=24 and z=12 Also,z2−xy=4 ⇒ xy=z2−4=144−4=140
(x−y)2=(x+y)2−4xy so,576−560=16 ∴ x−y=4 and x+y=24 On solving the above equations, we get 2y=20 ∴ y =10m
Most Upvoted Answer
The perimeters of both, a square and a rectangle are each equal to 48 ...
Given information:
- The perimeter of both a square and a rectangle is equal to 48 m.
- The difference between their areas is 4 m^2.
Let's solve the problem step by step:
Step 1: Identify the formulas:
- The perimeter of a square is given by P = 4s, where s is the side length.
- The perimeter of a rectangle is given by P = 2(l + b), where l is the length and b is the breadth.
- The area of a square is given by A = s^2.
- The area of a rectangle is given by A = l * b.
Step 2: Set up equations:
We are given that the perimeters of both the square and the rectangle are equal to 48 m. So we can write the following equations:
- For the square: 4s = 48
- For the rectangle: 2(l + b) = 48
Step 3: Solve for the side length of the square:
From the equation 4s = 48, we can solve for s:
4s = 48
Divide both sides by 4:
s = 12
Step 4: Solve for the length and breadth of the rectangle:
From the equation 2(l + b) = 48, we can simplify it to l + b = 24.
Since the perimeter of a square is equal to the perimeter of the rectangle, the side length of the square (s = 12) is equal to the sum of the length and breadth of the rectangle (l + b):
12 = l + b
Step 5: Find the difference between the areas of the square and rectangle:
- Area of the square = s^2 = 12^2 = 144 m^2
- Area of the rectangle = l * b = (12)(12) = 144 m^2
The difference between their areas is 144 m^2 - 144 m^2 = 0 m^2, which contradicts the given information that the difference is 4 m^2.
Conclusion:
There seems to be a mistake in the question. Based on the given information, it is not possible to determine the breadth of the rectangle.
- The perimeter of both a square and a rectangle is equal to 48 m.
- The difference between their areas is 4 m^2.
Let's solve the problem step by step:
Step 1: Identify the formulas:
- The perimeter of a square is given by P = 4s, where s is the side length.
- The perimeter of a rectangle is given by P = 2(l + b), where l is the length and b is the breadth.
- The area of a square is given by A = s^2.
- The area of a rectangle is given by A = l * b.
Step 2: Set up equations:
We are given that the perimeters of both the square and the rectangle are equal to 48 m. So we can write the following equations:
- For the square: 4s = 48
- For the rectangle: 2(l + b) = 48
Step 3: Solve for the side length of the square:
From the equation 4s = 48, we can solve for s:
4s = 48
Divide both sides by 4:
s = 12
Step 4: Solve for the length and breadth of the rectangle:
From the equation 2(l + b) = 48, we can simplify it to l + b = 24.
Since the perimeter of a square is equal to the perimeter of the rectangle, the side length of the square (s = 12) is equal to the sum of the length and breadth of the rectangle (l + b):
12 = l + b
Step 5: Find the difference between the areas of the square and rectangle:
- Area of the square = s^2 = 12^2 = 144 m^2
- Area of the rectangle = l * b = (12)(12) = 144 m^2
The difference between their areas is 144 m^2 - 144 m^2 = 0 m^2, which contradicts the given information that the difference is 4 m^2.
Conclusion:
There seems to be a mistake in the question. Based on the given information, it is not possible to determine the breadth of the rectangle.
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The perimeters of both, a square and a rectangle are each equal to 48 m and the difference between their areas is4m2. The breadth of the rectangle isa)10 mb)12 mc)14 md)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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