document.write( "Question 1186519: LEARNING ACTIVITY: Solve the Inequality! INSTRUCTIONS: Read and analyze the real-life problems. Perform the task by following the solving steps and answer the questions that follow. Brendan is a Plantito who has 48 m of fencing materials. He wants to make a garden whose area is greater than 108 m² but less than 150 m². Find the possible dimensions of his garden. How many possible garden can he make that Quadratic Inequalities. \n" ); document.write( "

Algebra.Com's Answer #817441 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "Let x be one side of the rectangular garden, in meters.\r\n" );
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document.write( "Then the other (adjacent) side length is  48/2 - x = 24 - x meters long.\r\n" );
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document.write( "The expression for the area is  x*(24-x)  square meters.\r\n" );
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document.write( "The inequality, which you want to impose on dimensions (on the area) is\r\n" );
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document.write( "    108 <= x*(24-x) <= 150  square meters,\r\n" );
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document.write( "or, which is the same\r\n" );
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document.write( "    108 <= -x^2 + 24x <= 150.\r\n" );
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document.write( "The quadratic function  -x^2 + 24x  has the maximum value of 144, which is achieved at x = 12.\r\n" );
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document.write( "It is less than 150, so inequality  x^2 + 24x <= 150  is valid for ANY VALUE of x, without restrictions.\r\n" );
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document.write( "The inequality  108 <= -x^2 + 24x  is valid at  6 <= x <= 18.\r\n" );
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document.write( "So, one side of the rectangular garden MUST SATISFY this restrictions.\r\n" );
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document.write( "The other (adjacent) side should be (24-x) meters long.\r\n" );
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document.write( "    (By the way, then the other (adjacent) side satisfies the same restrictions/inequalities (!) )\r\n" );
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document.write( "There are INFINITELY MANY possibilities under these conditions.\r\n" );
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