document.write( "Question 4129: One side of a rectangle is 7 cm longer than the other side. The diagonal is 8 cm longer than the shortest side of the rectangle. Find the dimensions of the rectangle. I am stuck and do not know how to solve this problem \n" ); document.write( "

Algebra.Com's Answer #1816 by ivankst(3) $\"\"$ $\"About$

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Let a and b be sides of a rectangle, and d a diagonal. Let $\"b%3Ca\"$ .
\n" ); document.write( "We have following equations:
\n" ); document.write( " $\"a=b%2B7\"$
\n" ); document.write( " $\"d=b%2B8\"$
\n" ); document.write( "By using Pythagorean theorem you can calculate that $\"d=sqrt%28a%5E2%2Bb%5E2%29\"$
\n" ); document.write( "So our system of equations becomes:
\n" ); document.write( " $\"a=b%2B7\"$
\n" ); document.write( " $\"sqrt%28a%5E2%2Bb%5E2%29=b%2B8\"$
\n" ); document.write( "If we put $\"a=b%2B7\"$ in second equation, we get:
\n" ); document.write( " $\"sqrt%28%28b%2B7%29%5E2%2Bb%5E2%29=b%2B8\"$
\n" ); document.write( " $\"%28b%2B7%29%5E2%2Bb%5E2=%28b%2B8%29%5E2\"$
\n" ); document.write( " $\"b%5E2%2B14b%2B49%2Bb%5E2=64%2B16b%2Bb%5E2\"$
\n" ); document.write( " $\"b%5E2-2b-15=0\"$
\n" ); document.write( " $\"b=%282%2B-sqrt%284-4%2A1%2A%28-15%29%29%29%2F2\"$
\n" ); document.write( " $\"b=%282%2B-sqrt%2864%29%29%2F2\"$
\n" ); document.write( " $\"b=%282%2B-8%29%2F2\"$
\n" ); document.write( " $\"b=5\"$ or $\"b=-3\"$
\n" ); document.write( "b cannot be a negative number, so b=5.
\n" ); document.write( "First eqaution gives us a:
\n" ); document.write( " $\"a=b%2B7\"$
\n" ); document.write( " $\"a=5%2B7\"$
\n" ); document.write( " $\"a=12\"$
\n" ); document.write( "So, sides of a rectangle are: (5,12).
\n" ); document.write( " \n" ); document.write( "

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