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Perimeter of a square is equal to the perimeter of the rectangle. If length and breadth of the rectangle is 24 cm and 20 respectively. Find the area of the square.
- a)484cm2
- b)490cm2
- c)516cm2
- d)520cm2
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Perimeter of a square is equal to the perimeter of the rectangle. If l...
To find the area of the square, we first need to determine the perimeter of both the square and the rectangle.
Perimeter of a square:
The perimeter of a square is calculated by adding up the lengths of all four sides. Since all sides of a square are equal, we can simply multiply the length of one side by 4 to find the perimeter.
Perimeter of a rectangle:
The perimeter of a rectangle is calculated by adding up the lengths of all four sides. In this case, the length and breadth of the rectangle are given as 24 cm and 20 cm respectively. Therefore, the perimeter of the rectangle can be found by adding these two lengths and then multiplying the sum by 2.
Now, let's calculate the perimeter of both the square and the rectangle.
Perimeter of the square = 4 × side length
Perimeter of the rectangle = 2 × (length + breadth)
Given that the perimeter of the square is equal to the perimeter of the rectangle, we can set up the following equation:
4 × side length = 2 × (length + breadth)
Substituting the given values of length and breadth into the equation:
4 × side length = 2 × (24 + 20)
4 × side length = 2 × 44
4 × side length = 88
side length = 88 / 4
side length = 22 cm
Now that we know the length of one side of the square is 22 cm, we can calculate its area.
Area of a square:
The area of a square is calculated by multiplying the length of one side by itself.
Area of the square = side length × side length
Area of the square = 22 cm × 22 cm
Area of the square = 484 cm²
Therefore, the area of the square is 484 cm², which corresponds to option A.
Perimeter of a square:
The perimeter of a square is calculated by adding up the lengths of all four sides. Since all sides of a square are equal, we can simply multiply the length of one side by 4 to find the perimeter.
Perimeter of a rectangle:
The perimeter of a rectangle is calculated by adding up the lengths of all four sides. In this case, the length and breadth of the rectangle are given as 24 cm and 20 cm respectively. Therefore, the perimeter of the rectangle can be found by adding these two lengths and then multiplying the sum by 2.
Now, let's calculate the perimeter of both the square and the rectangle.
Perimeter of the square = 4 × side length
Perimeter of the rectangle = 2 × (length + breadth)
Given that the perimeter of the square is equal to the perimeter of the rectangle, we can set up the following equation:
4 × side length = 2 × (length + breadth)
Substituting the given values of length and breadth into the equation:
4 × side length = 2 × (24 + 20)
4 × side length = 2 × 44
4 × side length = 88
side length = 88 / 4
side length = 22 cm
Now that we know the length of one side of the square is 22 cm, we can calculate its area.
Area of a square:
The area of a square is calculated by multiplying the length of one side by itself.
Area of the square = side length × side length
Area of the square = 22 cm × 22 cm
Area of the square = 484 cm²
Therefore, the area of the square is 484 cm², which corresponds to option A.
Community Answer
Perimeter of a square is equal to the perimeter of the rectangle. If l...
The perimeter of the square is equal to the perimeter of the rectangle.
- The rectangle has a length of 24 cm and a breadth of 20 cm.
- Calculate the perimeter of the rectangle:
- Perimeter = 2 × (24 cm + 20 cm) = 88 cm
- Since the perimeter of the square is the same, it is also 88 cm.
- Formula for the perimeter of a square: 4 × side length = 88 cm
- Solve for the side length:
- Side length = 88 cm ÷ 4 = 22 cm
- Calculate the area of the square:
- Area = side length × side length = 22 cm × 22 cm = 484 cm²
Therefore, the area of the square is 484 cm².
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