How Much will Increase in the Rectangle? If

The Length and Breadth of a rectangle are increased by 20% and 25% respectively. The increase in the area of the resulting rectangle will be:

  1. 25%
  2. 40%
  3. 45%
  4. 50%
Abdul Salam Newbie Asked on 7th August 2015 in Maths.
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  • 1 Answer(s)

    Answer: (4) 50 %

    Explanation:-
    Let the length of the rectangle is X m  & the breadth of the rectangle is Y m.

    Formula-
    The area of a rectangle = Length x breadth.

    Then, the area of the rectangle  = X  x Y
    = X Y m square.

    The Length and Breadth of a rectangle are increased by 20% and 25%.
    Then, the length of the rectangle = (X + X x 20/100)
    = ( X + X /5)
    = (5 X + X) / 5
    = 6 X / 5

    And the breadth of the rectangle = (Y + Y x 25/100)
    = (Y + Y/4)
    = (4 Y + Y )/4
    = 5 Y /4

    Then, the new area of the rectangle = 6 X x 5 Y / 5 x 4
    = 3 X Y / 2

    Increased area of rectangle = 3 X Y / 2 – X Y
    = (3 X Y – 2 X Y ) / 2
    =  X Y /2

    Percentage of increased area = X Y x 100/X  Y x 2
    = 100/2
    = 50 %
    The increase in the area of the resulting rectangle will be 50 %.

    Hence, the answer is (4) 50 %.

    Anurag Mishra Professor Answered on 7th August 2015.
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