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Read the passage below and solve the questions based on it The area of a square is equal lo the area of a rectangle. Moreover, the perimeter of the square is also equal to the perimeter of the rectangle,
Q.
The length of the rectangle is equal to the:
a)Breadth of the rectangle
b)Side of the square
c)Cannot be determined
d)Both [1] and [2]
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Read the passage below and solve the questions based on it The area of...
This is possible only when both the length and breadth of the rectangle are equal to the side of the square.
Most Upvoted Answer
Read the passage below and solve the questions based on it The area of...
Let a be the side of square and l , b are the length and breadth respectively.
a square =lb as per question and 4a=2(l+ b).
If l=b=a,then by the help of 2nd equation, we get 2(a+a)=2×2a=4a which is equal to L.H.S .hence proved.
a square =lb as per question and 4a=2(l+ b).
If l=b=a,then by the help of 2nd equation, we get 2(a+a)=2×2a=4a which is equal to L.H.S .hence proved.
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Read the passage below and solve the questions based on it The area of...
The Question:
The question asks for the length of the rectangle, given that the area and perimeter of the square are equal to the area and perimeter of the rectangle. The options provided are:
a) Breadth of the rectangle
b) Side of the square
c) Cannot be determined
d) Both [1] and [2]
Understanding the Problem:
To solve this question, we need to analyze the relationships between the area and perimeter of the square and rectangle. We also need to consider the properties of squares and rectangles.
Properties of Squares:
- A square has all four sides equal in length.
- The area of a square is calculated by multiplying the length of one side by itself.
- The perimeter of a square is calculated by multiplying the length of one side by 4.
Properties of Rectangles:
- A rectangle has opposite sides equal in length and all four angles equaling 90 degrees.
- The area of a rectangle is calculated by multiplying the length and breadth (or width) of the rectangle.
- The perimeter of a rectangle is calculated by adding the lengths of all four sides.
Analysis and Solution:
Since the area of the square is equal to the area of the rectangle, we can set up the following equation:
Side of the square * Side of the square = Length of the rectangle * Breadth of the rectangle
Similarly, since the perimeter of the square is equal to the perimeter of the rectangle, we can set up the following equation:
4 * Side of the square = 2 * (Length of the rectangle + Breadth of the rectangle)
Now, let's analyze the given options:
a) Breadth of the rectangle: This option suggests that the length of the rectangle is equal to its breadth. However, this cannot be determined based on the information given.
b) Side of the square: This option suggests that the length of the rectangle is equal to the side of the square. Based on the equations above, this option is valid.
c) Cannot be determined: This option suggests that the length of the rectangle cannot be determined based on the given information. However, as shown above, we can determine the relationship between the length of the rectangle and the side of the square.
d) Both [1] and [2]: This option suggests that both the breadth of the rectangle and the side of the square are equal to the length of the rectangle. Based on the equations above, this option is valid.
Therefore, the correct answer is option 'D' - Both [1] and [2].
The question asks for the length of the rectangle, given that the area and perimeter of the square are equal to the area and perimeter of the rectangle. The options provided are:
a) Breadth of the rectangle
b) Side of the square
c) Cannot be determined
d) Both [1] and [2]
Understanding the Problem:
To solve this question, we need to analyze the relationships between the area and perimeter of the square and rectangle. We also need to consider the properties of squares and rectangles.
Properties of Squares:
- A square has all four sides equal in length.
- The area of a square is calculated by multiplying the length of one side by itself.
- The perimeter of a square is calculated by multiplying the length of one side by 4.
Properties of Rectangles:
- A rectangle has opposite sides equal in length and all four angles equaling 90 degrees.
- The area of a rectangle is calculated by multiplying the length and breadth (or width) of the rectangle.
- The perimeter of a rectangle is calculated by adding the lengths of all four sides.
Analysis and Solution:
Since the area of the square is equal to the area of the rectangle, we can set up the following equation:
Side of the square * Side of the square = Length of the rectangle * Breadth of the rectangle
Similarly, since the perimeter of the square is equal to the perimeter of the rectangle, we can set up the following equation:
4 * Side of the square = 2 * (Length of the rectangle + Breadth of the rectangle)
Now, let's analyze the given options:
a) Breadth of the rectangle: This option suggests that the length of the rectangle is equal to its breadth. However, this cannot be determined based on the information given.
b) Side of the square: This option suggests that the length of the rectangle is equal to the side of the square. Based on the equations above, this option is valid.
c) Cannot be determined: This option suggests that the length of the rectangle cannot be determined based on the given information. However, as shown above, we can determine the relationship between the length of the rectangle and the side of the square.
d) Both [1] and [2]: This option suggests that both the breadth of the rectangle and the side of the square are equal to the length of the rectangle. Based on the equations above, this option is valid.
Therefore, the correct answer is option 'D' - Both [1] and [2].
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Read the passage below and solve the questions based on it The area of a square is equal lo the area of a rectangle. Moreover, the perimeter of the square is also equal to the perimeter of the rectangle,Q.The length of the rectangle is equal to the:a)Breadth of the rectangleb)Side of the squarec)Cannot be determinedd)Both [1] and [2]Correct answer is option 'D'. Can you explain this answer?
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Read the passage below and solve the questions based on it The area of a square is equal lo the area of a rectangle. Moreover, the perimeter of the square is also equal to the perimeter of the rectangle,Q.The length of the rectangle is equal to the:a)Breadth of the rectangleb)Side of the squarec)Cannot be determinedd)Both [1] and [2]Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Read the passage below and solve the questions based on it The area of a square is equal lo the area of a rectangle. Moreover, the perimeter of the square is also equal to the perimeter of the rectangle,Q.The length of the rectangle is equal to the:a)Breadth of the rectangleb)Side of the squarec)Cannot be determinedd)Both [1] and [2]Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the passage below and solve the questions based on it The area of a square is equal lo the area of a rectangle. Moreover, the perimeter of the square is also equal to the perimeter of the rectangle,Q.The length of the rectangle is equal to the:a)Breadth of the rectangleb)Side of the squarec)Cannot be determinedd)Both [1] and [2]Correct answer is option 'D'. Can you explain this answer?.
Read the passage below and solve the questions based on it The area of a square is equal lo the area of a rectangle. Moreover, the perimeter of the square is also equal to the perimeter of the rectangle,Q.The length of the rectangle is equal to the:a)Breadth of the rectangleb)Side of the squarec)Cannot be determinedd)Both [1] and [2]Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Read the passage below and solve the questions based on it The area of a square is equal lo the area of a rectangle. Moreover, the perimeter of the square is also equal to the perimeter of the rectangle,Q.The length of the rectangle is equal to the:a)Breadth of the rectangleb)Side of the squarec)Cannot be determinedd)Both [1] and [2]Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Read the passage below and solve the questions based on it The area of a square is equal lo the area of a rectangle. Moreover, the perimeter of the square is also equal to the perimeter of the rectangle,Q.The length of the rectangle is equal to the:a)Breadth of the rectangleb)Side of the squarec)Cannot be determinedd)Both [1] and [2]Correct answer is option 'D'. Can you explain this answer?.
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