Find the Length and Width of the Rectangle ?

If one side of a square is doubled in length and the adjacent side is decreased by four centimeters, then the area of the resulting rectangle is 48 square centimeters larger than that of the original square. Find the length and width of the rectangle.

  1. 12 cm, 8 cm
  2. 11cm, 9 cm
  3. 24 cm 8 cm
  4. 24 cm, 12 cm
Anurag Mishra Professor Asked on 26th November 2015 in Maths.
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  • 1 Answer(s)

    Answer: (3) 24 cm, 8 cm 

    Explanation:-
    Let the side of a square be X meters.
    Then, the area of a square = X² meters

    One side of a square is doubled in length and the adjacent side is decreased by 4 cm.
    Then, the length of a new rectangle = 2 X cm and the width of a new rectangle = (X – 4) cm

    Therefore, the area of a new rectangle = 2 X . (X – 4)
    = 2 X² – 2 x 4 X
    = (2 X² – 8 X) cm square

    Then, the area of the resulting rectangle is 48 square centimeters larger than that of the original square.

    So, (2 X² – 8 X) – X² = 48
    2 X² – 8 X – X² = 48
    X² – 8 X – 48 = 0
    X² – 12 X + 4 X – 48 = 0
    X (X – 12) + 4( X – 12) = 0
    (X + 4) (X – 12)= 0
    X – 12 = 0
    X = 12

    Then, the length of the new rectangle = 2 x 12
    = 24 cm
    And, the width of the new rectangle = 12 – 4
    = 8 cm

    Hence, the answer is (3) 24 cm, 8 cm.

    Anurag Mishra Professor Answered on 26th November 2015.
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