document.write( "Question 201933: The diagonal of a square is 2 meters longer than a side. Find the length of a side. \n" ); document.write( "

Algebra.Com's Answer #152166 by Earlsdon(6294) $\"\"$ $\"About$

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Let s = the length of the side of the square, then the length of the diagonal is:
\n" ); document.write( " $\"s%2B2%29\"$ .
\n" ); document.write( "Using the Pythagorean relationship for the sides of a right triangle ( $\"c%5E2+=+a%5E2%2Bb%5E2\"$ ) in which c is the diagonal of the square, so: $\"c+=+s%2B2\"$ and...
\n" ); document.write( " $\"%28s%2B2%29%5E2+=+s%5E2%2Bs%5E2\"$ Expand the left side.
\n" ); document.write( " $\"s%5E2%2B4s%2B4+=+2%2As%5E2\"$ Subtract $\"2%2As%5E2\"$ from both sides.
\n" ); document.write( " $\"-s%5E2%2B4s%2B4+=+0\"$ Use the quadratic formula to solve: $\"s+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$ where: a = -1, b = 4, and c = 4
\n" ); document.write( " $\"s+=+%28-4%2B-sqrt%284%5E2-4%28-1%29%284%29%29%29%2F2%28-1%29\"$
\n" ); document.write( " $\"s+=+%28-4%2B-sqrt%2816-%28-16%29%29%29%2F%28-2%29\"$
\n" ); document.write( " $\"s+=+%28-4%2B-sqrt%2832%29%29%2F%28-2%29\"$
\n" ); document.write( " $\"highlight%28s+=+2%2B2sqrt%282%29%29\"$ or $\"highlight_green%28s+=+2-2sqrt%282%29%29\"$ Discard the negative (green) solution as the length of the side of a square is a positive value (red).
\n" ); document.write( " $\"+s+=+2%2B2sqrt%282%29\"$ This is the exact value of the side of the square.
\n" ); document.write( " $\"+s+=+4.828\"$ This is the approximate value. \n" ); document.write( "

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