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23 April, 05:47

The Length of a standard jewel case is 7cm more than its width. The area of the rectangular top of the case is 408cm. Find the length and width of the jewel Case

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  1. 23 April, 09:03
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    The length of the case is 24 cm and its width is 17cm.

    Step-by-step explanation:

    The Length of a standard jewel case is 7cm more than its width.

    Let the length be represented by L and the width be represented by W, this means that:

    L = 7 + W

    The area of the rectangular top of the case is 408cm². The area od a rectangle is given as:

    A = L * W

    Since L = 7 + W:

    A = (7 + W) * W = 7W + W²

    The area is 408 cm², hence:

    408 = 7W + W²

    Solving this as a quadratic equation:

    => W² + 7W - 408 = 0

    W² + 24W - 17W - 408 = 0

    W (W + 24) - 17 (W + 24) = 0

    (W - 17) (W + 24) = 0

    => W = 17cm or - 24 cm

    Since width cannot be negative, the width of the case is 17 cm.

    Hence, the length, L, is:

    L = 7 + 17 = 24cm.

    The length of the case is 24 cm and its width is 17cm.
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