document.write( "Question 1199222: A rectangular plot, 4 meters by 8 meters, is to be used for a garden. The owner decides to put a pavement of uniform width inside the entire border so that 12 square meters of the plot is left for flowers. How wide should the pavement be? \n" ); document.write( "

Algebra.Com's Answer #832991 by Shin123(626) $\"\"$ $\"About$

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Let the pavement width be $\"x\"$ . Then, the dimensions of the rectangle that is left is $\"4-2x\"$ by $\"8-2x\"$ . We know that this equals $\"12\"$ , so we have $\"%284-2x%29%2A%288-2x%29=12\"$ . Expanding, we get $\"4x%5E2-24x%2B32=12\"$ . Subtracting $\"12\"$ from both sides, we get $\"4x%5E2-24x%2B20=0\"$ . To simplify the quadratic, we can divide both sides by $\"4\"$ to get $\"x%5E2-6x%2B5=0\"$ . We can easily factor this to get $\"%28x-1%29%28x-5%29=0\"$ . Note that $\"x=5\"$ won't work in our case because the dimensions of the rectangle can't be negative. Therefore, the pavement should be $\"1\"$ meter long. \n" ); document.write( "

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