document.write( "Question 1124076: The length of a rectangle vegetable garden is 5 meters more than its width. Find the dimensions of the vegetable garden if its area is 204 square meters \n" ); document.write( "

Algebra.Com's Answer #740436 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Let x be the width; then the length is x+5. Then the area is length times width:

\n" ); document.write( " $\"x%28x%2B5%29+=+204\"$
\n" ); document.write( " $\"x%5E2%2B5x-204+=+0\"$
\n" ); document.write( " $\"x%2B17%29%28x-12%29+=+0\"$
\n" ); document.write( " $\"x+=+-17\"$ or $\"x+=+12\"$

\n" ); document.write( "Obviously -17 is not a valid width. So the width is 12m and the length is 17m.

\n" ); document.write( "To solve that problem algebraically, as above, we had to factor the x^2+5x-204 by finding two number whose product is 204 and whose difference is 5.

\n" ); document.write( "But that is exactly what the problem asks us to do... so the formal algebra doesn't help us any.

\n" ); document.write( "The easiest way to solve this problem is to forget the algebra and straight away look for two numbers whose product is 204 and whose difference is 5. A little trial and error finds the numbers 12 and 17. \n" ); document.write( "

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