algebra

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The area of a rectangle remains unchanged when it is made 5cm shorter and 5cm wider or when it is made 2cm longer and 1cm narrower. Its area, in square cm, is:

  • algebra -

    LW = (L+5)*(W-5)
    LW = LW + 5W -5L -25
    5L - 5W = 25

    (L +2)(W-1) = L W
    -L + 2W = 2
    -5L +10W = 10

    Combining equations 3 and 6,
    5W = 35
    W = 7
    L = 2W-2 = 12

    Area = 84 cm^2

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