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17 March, 05:05

A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Round to the nearest hundredth. Enter your answer in the box.

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  1. 17 March, 05:32
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    36.50 in

    Step-by-step explanation:

    The length of the diagonal of the square base is found using the Pythagorean Theorem: d^2 = (12 in) ^2 + (12 in) ^2, or d = √2 * (12 in), or d = 12√2 in.

    We use the Pythagorean Theorem again to find the length of the interior diagonal of the box:

    [12√2 in]² + [ (12 in) ² + (30 in) ² = (interior diagonal) ²

    This works out to (interior diagonal) ² = 288 + 144 + 900 inches², or

    (interior diagonal) ² = 1332 in²

    Then the interior diagonal is √1332 in, or approximately 36.50 in.
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