document.write( "Question 452744: An airplane ticket has an area of 70 square centimeters. Its perimeter is 34 centimeters. What are the dimensions of the ticket? \n" ); document.write( "

Algebra.Com's Answer #311152 by ilana(307) $\"\"$ $\"About$

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If it's length and width are x and y, then its area is xy and its perimeter is 2x + 2y. So you can write 2 equations and solve the system.
\n" ); document.write( "xy = 70
\n" ); document.write( "2x + 2y = 34
\n" ); document.write( "Substitute 70/y for x (from the first equation) into the second equation.
\n" ); document.write( "2(70/y) + 2y = 34
\n" ); document.write( "140/y + 2y = 34
\n" ); document.write( "Multiply everything by y.
\n" ); document.write( "140 + 2y^2 = 34y
\n" ); document.write( "2y^2 - 34y + 140 = 0
\n" ); document.write( "Divide everything by 2.
\n" ); document.write( "y^2 - 17y + 70 = 0
\n" ); document.write( "(y - 10)(y - 7) = 0
\n" ); document.write( "y = 7 or 10
\n" ); document.write( "So the dimensions are 7 cm by 10 cm. \n" ); document.write( "

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