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27 October, 11:11

The perimeter of a playing card is 28 centimeters. The area is 48 square centimeters. What are the dimensions of the playing card?

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  1. 27 October, 11:36
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    Let length be l

    and breadth be b

    perimeter = 28

    2 (l+b) = 28

    l + b = 14

    l = 14 - b

    area = 48

    l x b = 48

    (14 - b) b = 48

    14b - b^2 = 48

    b^2 - 14b + 48 = 0

    b^2 - 6b - 8b + 48 = 0

    b (b - 6) - 8 (b - 6) = 0

    (b-8) (b-6) = 0

    so

    either b = 8 or b = 6

    if b = 8

    l = 14 - 8 = 6

    (not possible as length cannot be smaller than breadth)

    so

    breadth = 6

    length = 8
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