document.write( "Question 1067205: The side of a square equals the width of a rectangle. The length of the rectangle is 10 meters longer than its width. The sum of the areas of the square and the rectangle is 208 square meters. Find the side of the square. \n" ); document.write( "

Algebra.Com's Answer #682395 by chen.aavaz(62) $\"\"$ $\"About$

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\n" ); document.write( "Side of square a = w
\n" ); document.write( "Length of rectangle $\"l=w%2B10\"$
\n" ); document.write( "Area of square $\"A+=+a%5E2+=+w%5E2\"$
\n" ); document.write( "Area of rectangle $\"R+=+l%2Aw+=+%28w%2B10%29%2Aw\"$
\n" ); document.write( "Sum of A+R=208 so
\n" ); document.write( " $\"w%5E2%2B%28w%2B10%29%2Aw=208\"$
\n" ); document.write( " $\"w%5E2%2Bw%5E2%2B10w-208=0\"$
\n" ); document.write( " $\"2w%5E2%2B10w-208=0\"$
\n" ); document.write( " $\"w%5E2%2B5w-104=0\"$
\n" ); document.write( " $\"w=%28-5%2B-sqrt%285%5E2-4%2A1%2A104%29%29%2F%282%2A1%29\"$
\n" ); document.write( "The equation has two roots, w=8 and w=-13. Obviously we keep only the positive.
\n" ); document.write( "So the side of the square is 8m. \n" ); document.write( "

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