document.write( "Question 452194: a rectangle has a length of 18 inches more than three times its height. the perimeter is 428, what are the dimensions? \n" ); document.write( "
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\"a rectangle has a length of 18 inches more than three times its height.\"
\n" ); document.write( "height: x
\n" ); document.write( "\"three times its height\": 3x
\n" ); document.write( "\"18 inches more than three times its height\": 3x + 18
\n" ); document.write( "therefore, length: 3x + 18
\n" ); document.write( "The perimeter or a rectangle is denoted as 2(length) + 2(height). If the height is x and the length is 3x + 18, then the perimeter is 2(3x + 18) + 2(x). Since the problem states that the perimeter is 428 inches:
\n" ); document.write( "2(3x + 18) + 2x = 428
\n" ); document.write( "Distribut the 2 into the 3x and 18:
\n" ); document.write( "6x + 36 + 2x = 428
\n" ); document.write( "Add like terms (6x and 2x):
\n" ); document.write( "8x + 36 = 428
\n" ); document.write( "Subtract 36 from both sides:
\n" ); document.write( "8x = 392
\n" ); document.write( "Divide both sides by 8:
\n" ); document.write( "x = 49
\n" ); document.write( "So, the height of the rectangle is 49 inches. You can plug this value for x into the expression for length (3x + 18) to find the length of the rectangle.
\n" ); document.write( "3x + 18
\n" ); document.write( "3(49) + 18
\n" ); document.write( "147 + 18
\n" ); document.write( "165
\n" ); document.write( "So, the length of the rectangle is 165 inches.
\n" ); document.write( "==> Therefore, the height of the rectangle is 49 inches and the length of the rectange is 165 inches. \n" ); document.write( "
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