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27 March, 06:05

A rectangular box has a length of 3 inches, a width of 2 inches, and a height of 4 inches. Find the dimensions of the three similar boxes: one that has a length of 6 inches, one that has a width of 6 inches, and one that has a heght of 6 inches.

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  1. 27 March, 06:27
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    Step-by-step explanation:

    When two plane figures are similar in size, it means that there is a constant ratio between the size of the corresponding sides.

    A rectangular box has a length of 3 inches, a width of 2 inches, and a height of 4 inches.

    1) if a similar box has a length of 6 inches, it means that the ratio of its length to that of the original rectangle would be

    6/3 = 2

    The width of the new rectangle would be 2 * 2 = 4 inches.

    The height of the new rectangle would be 4 * 2 = 8 inches.

    2) if a similar box has a width of 6 inches, it means that the ratio of its width to that of the original rectangle would be

    6/2 = 3

    The length of the new rectangle would be 3 * 3 = 9 inches.

    The height of the new rectangle would be 4 * 3 = 12 inches.

    3) if a similar box has a height of 6 inches, it means that the ratio of its height to that of the original rectangle would be

    6/4 = 1.5

    The length of the new rectangle would be 3 * 1.5 = 4.5 inches.

    The width of the new rectangle would be 2 * 1.5 = 3 inches.
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