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The length of a rectangle is two times that of a square whose perimeter is 80 cm. If breadth of the rectangle is 20 cm, then the area (in cm2) of the rectangle exceeds the area of the square by
  • a)
    100 sq.cm
  • b)
    150 sq.cm
  • c)
    300 sq.cm
  • d)
    400 sq.cm
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The length of a rectangle is two times that of a square whose perimete...
Side of the square = 80/4 = 20 cm
Area of the square = 20 x 20 = 400 sq.cm
Length of the rectangle = 20 x 2 = 40 cm
Breadth of the rectangle = 20 cm
Area of the rectangle = 20 x 40 = 800 sq.cm
The area of rectangle exceeds the area of square by (800 - 400) = 400 sq.cm
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Community Answer
The length of a rectangle is two times that of a square whose perimete...
Given:
- Perimeter of the square = 80 cm
- Breadth of the rectangle = 20 cm

To find:
- The area (in cm2) by which the area of the rectangle exceeds the area of the square

Solution:

Step 1: Finding the side of the square
- The perimeter of a square is given by the formula: Perimeter = 4 * side
- Given that the perimeter of the square is 80 cm, we can write the equation as:
80 = 4 * side
Dividing both sides by 4, we get:
side = 80/4 = 20 cm

Step 2: Finding the length of the rectangle
- The length of the rectangle is given as twice the side of the square.
- Therefore, the length of the rectangle = 2 * side = 2 * 20 cm = 40 cm

Step 3: Finding the area of the square
- The area of a square is given by the formula: Area = side * side
- Substituting the value of side as 20 cm, we get:
Area of the square = 20 * 20 = 400 sq.cm

Step 4: Finding the area of the rectangle
- The area of a rectangle is given by the formula: Area = length * breadth
- Substituting the values of length and breadth as 40 cm and 20 cm respectively, we get:
Area of the rectangle = 40 * 20 = 800 sq.cm

Step 5: Finding the difference in area
- The difference in area between the rectangle and the square is given by:
Difference in area = Area of rectangle - Area of square
Difference in area = 800 - 400 = 400 sq.cm

Therefore, the area of the rectangle exceeds the area of the square by 400 sq.cm. Hence, the correct answer is option 'D'.
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The length of a rectangle is two times that of a square whose perimeter is 80 cm. If breadth of the rectangle is 20 cm, then the area (in cm2) of the rectangle exceeds the area of the square bya)100 sq.cmb)150 sq.cmc)300 sq.cmd)400 sq.cmCorrect answer is option 'D'. Can you explain this answer?
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