document.write( "Question 1009529: An open box is made from a rectangular piece of cardboard measuring 12 by 16 inches by cutting identical squares from the corners and turning up the sides. describe the possible lengths of the sides of the removed squares is the volume of the open is not to exceed 540 cubic inches. \n" ); document.write( "

Algebra.Com's Answer #625101 by josgarithmetic(39620) $\"\"$ $\"About$

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If x is the length of each side of square to remove, then the area for the base of the box is $\"%2812-2x%29%2816-2x%29\"$ and then the volume is $\"x%2812-2x%29%2816-2x%29%3C=540\"$ , according to the inequality for the description. The flaps created, which are folded up to form the box, is the height, x.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%2812-2x%29%2816-2x%29-540%3C=0\"$ , importantly, came from the first expression being LESS THAN OR EQUAL TO the given volume limit of 540 cubic inches.\r
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\n" ); document.write( "\n" ); document.write( " $\"2%2A2x%286-x%29%288-x%29-4%2A135%3C=0\"$ \r
\n" ); document.write( "\n" ); document.write( "Divide both members by 4,\r
\n" ); document.write( "\n" ); document.write( " $\"x%286-x%29%288-x%29-135%3C=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%2848-14x%2Bx%5E2%29-135%3C=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight_green%28x%5E3-14x%5E2%2B48x-135%3C=0%29\"$ ------Rational Roots Theorem and synthetic division if you want , but graphing tool shows ONE root of about x=10.7, which is not useful; not enough size on either dimension of the cardboard to cut that size square. Any possible value for x which could be made MUST BE LESS THAN 6 inches, and based on what is seen on a graph (using graphing tool), any value x at 6 or less, will satisfy the inequality. \n" ); document.write( "

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