document.write( "Question 898081: The length and the width of a rectangular floor a m and b m. Solve for a and b, given the following
\n" ); document.write( "information:
\n" ); document.write( "• If the length and the width each increases with 1 m, the area will increase with 9 m^2.
\n" ); document.write( "• If the length decreases with 0.5 m and the width increases with 4 m, the area is doubled. \n" ); document.write( "

Algebra.Com's Answer #544542 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
The length and the width of a rectangular floor a m and b m. Solve for a and b, given the following
\n" ); document.write( "information:
\n" ); document.write( "• If the length and the width each increases with 1 m, the area will increase with 9 m^2.
\n" ); document.write( "• If the length decreases with 0.5 m and the width increases with 4 m, the area is doubled.
\n" ); document.write( "


\n" );
document.write( "Length:  a
\n" );
document.write( "Width:   b
\n" );
document.write( "Area: ab\r
\n" );
document.write( "\n" );
document.write( "An increase in length, by 1 results in new length being: a + 1
\n" );
document.write( "An increase in width, by 1 results in new width being: b + 1
\n" );
document.write( "If new area increases by 9, then: (a + 1)(b + 1) = ab + 9
\n" );
document.write( "ab + a + b + 1 = ab + 9
\n" );
document.write( "ab - ab + a + b = 9 - 1
\n" );
document.write( "a + b = 8____a = 8 - b ------ eq (i)\r
\n" );
document.write( "\n" );
document.write( "A decrease in length, by .5 results in new length being: a - .5
\n" );
document.write( "An increase in width, by 4 results in new width being: b + 4
\n" );
document.write( "If new area is doubled, then new area becomes: 2ab 
\n" );
document.write( "Therefore, (a - .5)(b + 4) = 2ab
\n" );
document.write( "ab + 4a - .5b - 2 = 2ab
\n" );
document.write( "2ab - ab - 4a + .5b = - 2
\n" );
document.write( "ab - 4a + .5b = - 2 ------- eq (ii)\r
\n" );
document.write( "\n" );
document.write( "b(8 - b) - 4(8 - b) + .5b = - 2 ------ Substituting 8 - b for a on eq (ii)
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( " ------- Multiplying by 2 to clear decimal
\n" );
document.write( "Using the quadratic equation,
\n" );
document.write( "width, or   OR    (ignore as a = 8 - b, which would result in a negative value for a)
\n" );
document.write( "a = 8 - 3.2396 ------- Substituting 3.2396 for b in eq (i)
\n" );
document.write( "Length, or 
\n" );
document.write( "You can do the check!! \r
\n" );
document.write( "\n" );
document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
\n" );
document.write( "Further help is available, online or in-person, for a fee, obviously. \r
\n" );
document.write( "\n" );
document.write( "For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL
\n" );
document.write( "MATH and HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra, 
\n" );
document.write( "Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE,
\n" );
document.write( "GRE, CLEP, and the TASC/GED, you can visit: http://asvabstudyzone.freeforums.net/. \n" );
document.write( "

\n" );