document.write( "Question 413629: the dog yard has an area of 12 square meters. which of the following perimeters,in meters,will Not give an area of 12 square meters? A.14 meters B.16 meters C.24 meters D. 26 meters \n" ); document.write( "

Algebra.Com's Answer #290285 by richard1234(7193) $\"\"$ $\"About$

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Let x and 12/x be the dimensions of the dog yard. We wish to check which of\r
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\n" ); document.write( "\n" ); document.write( " $\"x+%2B+%2812%2Fx%29+=+k\"$ , k ∈ {14, 16, 24, 26} has no positive real solution x.\r
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\n" ); document.write( "\n" ); document.write( "The above equation is equivalent to $\"x%5E2+%2B+12+=+kx\"$ --> $\"x%5E2+-+kx+%2B+12+=+0\"$ . The discriminant is $\"b%5E2+-+4ac+=+k%5E2+-+48\"$ . As all the numbers k are greater than $\"sqrt%2848%29\"$ , all of these k produce two real solutions x. Also, by the quadratic formula, $\"x+=+%28k+%2B-+sqrt%28k%5E2+-+48%29%29%2F2\"$ . It can be checked that for k ∈ {14, 16, 24, 26}, there is a positive, real solution for x, so none of the answers can be correct (all choices can yield an area of 12 sq m).\r
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\n" ); document.write( "\n" ); document.write( "You might want to include all information in the problem. For example, do the sides of the yard have to be integers? \n" ); document.write( "

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