document.write( "Question 154169: Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what are its dimensions? \n" ); document.write( "

Algebra.Com's Answer #113473 by orca(409) $\"\"$ $\"About$

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Let x be the width, then the length is 3x.
\n" ); document.write( "So its area = length*width = 3x*x = 3x^2.
\n" ); document.write( "As the area is 75, we have
\n" ); document.write( " $\"3x%5E2=75\"$
\n" ); document.write( "Solving the quadratic equation, we have
\n" ); document.write( " $\"x%5E2=25\"$ (divide both sides by 3)
\n" ); document.write( "So
\n" ); document.write( " $\"x=sqrt%2825%29=5\"$ or $\"x=-sqrt%2825%29=-5\"$
\n" ); document.write( "As the width can not be negative, the solution x = -5 is rejected.
\n" ); document.write( "Thus the width is 5, and the length is 3x=3*5 = 15.\r
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