The area of a rectangle is 60 units. If the length and breadth are reduced respectively by 6 units

The area of a rectangle is 60 units. If the length and breadth are reduced respectively by 6 units and 2 units, it becomes a square. Then the area of the square (in sq. units) is

  1. 4
  2. 9
  3. 16
  4. 36
Anurag Mishra Professor Asked on 20th April 2016 in Maths.
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  • 1 Answer(s)

    Answer: (3) 16 

    Solution:-
    Let the length and breadth of the rectangle be X and Y.

    The area of a rectangle is 60 units.
    Then, X Y = 60

    If the length and breadth are reduced respectively  by 6 units and 2 units.
    Then, X – 6 = Y – 2
    X – Y = 6 – 2
    X – Y = 4 ………………………. (1)
    Square on both side,
    (X – Y)^2 = X^2 + Y^2 – 2 X Y
    4^2 = X^2 + Y^2 – 2 x 60
    X^2 + Y^2 = 120 + 16
    X^2 + Y^2 = 136 …………………… (2)

    Again,
    (X + Y)^2 = X^2 + Y^2 + 2 X Y
    From equation (2),
    (X + Y)^2 = 136 + 2 x 60
    = 136 + 120
    (X + Y)^2 = 256
    Square root on both side,
    X + Y = 16         ………………(3)

    Add equation (1) & (3),
    X – Y + X + Y = 16 + 4
    2 X = 20
    X = 10

    Put the value of X = 10 in equation (3),
    10 + Y = 16
    Y = 16 – 10
    Y = 6

    Then, length and breadth of rectangle are 10 cm and 6 .

    If the length and breadth are reduced respectively  by 6 units and 2 units.
    Then, the side of the square = 10 – 6 = 4

    So, the are of the square = 4 x 4
    = 16 units

    Hence, the correct answer is option (3) 16.

     

    Anurag Mishra Professor Answered on 22nd April 2016.
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