What is the area of the rectangle:

If the length of a rectangle is increased by 20 % and width of the same rectangele decreased by 20 %, then the area of the rectangle:

  1. Decreases by 20%
  2. Decreases by 4%
  3. Is unchanged
  4. Increases by 20 %
Harsh Vardhan Professor Asked on 25th October 2015 in Maths.
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  • 1 Answer(s)

    Answer:  (2)  Decreased by 4 %

    Explanation:-
    Let the length of a rectangle is  X m and width of the same rectangle is Y m
    Then, the area of the rectangle = X Y square m

    If the length of a rectangle is increased by 20 %
    Then, the length of a new rectangle = X + X x 20/100
    = X + X/5
    = (5 x + X)/5
    = 6 X/5 m

    If the breadth of the rectangle is decreased by 20 %
    Then, the new breadth of the rectangle = Y – Y  x 20/100
    = Y – Y/5
    = (5 Y – Y)/5
    = 4 Y/5

    Then, the area of new rectangle = 6 X x 4 Y /5 x
    = 24 X Y /25

    Decreased area = X Y- 24 X Y /25
    = (25 X Y – 24 X Y)/25
    = X Y/25

    Decreased area in percentage = X Y x 100/25 x X Y
    = 100/25 %
    = 4 %

    Then, the area of a rectangle is decreased by 4%.

    Hence, the answer is (2) 4%.

    Anurag Mishra Professor Answered on 25th October 2015.
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