document.write( "Question 1017069: an equilateral triangle and a rectangle have the same perimeter. the length of a rectangle is 3 cm less tan twice the width. each side of a triangle is 12 cm. find the area of the rectangle. \n" ); document.write( "

Algebra.Com's Answer #633404 by ikleyn(52779) $\"\"$ $\"About$

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\n" ); document.write( "An equilateral triangle and a rectangle have the same perimeter. The length of a rectangle is 3 cm less tan twice the width.
\n" ); document.write( "Each side of a triangle is 12 cm. find the area of the rectangle.
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document.write( "The perimeter is 3*12 = 36 cm, calculated for the triangle.\r\n" );
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document.write( "The perimeter of the rectangle is the same: 36 cm.\r\n" );
document.write( "So, the sum of the measures of two its consecutive sides is  = 18, which gives you an equation\r\n" );
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document.write( "x + y = 18.   (1)\r\n" );
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document.write( "It is the first equation. The second equation is \r\n" );
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document.write( "x = 2y - 3,   (2)\r\n" );
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document.write( "according to the condition. Substitute the expression (2) into (1) to eliminate x. You will get\r\n" );
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document.write( "2y - 3 + y = 18,  --->  3y = 18+3 = 21  --->  y =  = 7 cm.\r\n" );
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document.write( "Thus one side of the rectangle is 7 cm long.\r\n" );
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document.write( "Then the other side of the rectangle is 18 - 7 = 11 cm.\r\n" );
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document.write( "Then its area is 7*11 = 77 .\r\n" );
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