document.write( "Question 551992: Could you please help me solve this...
\n" ); document.write( "The sides of a rectangle are A: 5X, B:5Y, C:7Y+7, D: 2X+6
\n" ); document.write( "What are the values of the variables and the length of the sides. \n" ); document.write( "
Algebra.Com's Answer #360112 by Theo(13342)\"\" \"About 
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your rectangle is:
\n" ); document.write( "ABCD
\n" ); document.write( "side AB is equal to 5x.
\n" ); document.write( "side BC is equal to 5y.
\n" ); document.write( "side CD is equal to 7y+7
\n" ); document.write( "side AD is equal to 2x+6
\n" ); document.write( "side AB is opposite side CD.
\n" ); document.write( "side BC is opposite side AD
\n" ); document.write( "opposite sides of a rectangle are equal.
\n" ); document.write( "this means that:
\n" ); document.write( "5x = 7y+7
\n" ); document.write( "5y = 2x+6
\n" ); document.write( "solve for y in each equation to get:
\n" ); document.write( "y = (5x-7)/7 (first equation)
\n" ); document.write( "y = (2x+6)/5 (second equation)
\n" ); document.write( "since they are both equal to y, then they are both equal to each other and we get:
\n" ); document.write( "(5x-7)/7 = (2x+6)/5
\n" ); document.write( "multiply both sides of this equation by 35 to get:
\n" ); document.write( "5(5x-7) = 7(2x+6)
\n" ); document.write( "simplify to get:
\n" ); document.write( "25x - 35 = 14x + 42
\n" ); document.write( "subtract 14x from both sides of this equation and add 35 to both sides of this equation to get:
\n" ); document.write( "11x = 77
\n" ); document.write( "divide both sides of this equation by 11 to get:
\n" ); document.write( "x = 7
\n" ); document.write( "substitute for x in either original equation to get:
\n" ); document.write( "y = 4
\n" ); document.write( "your solution is that x = 7 and y = 4.
\n" ); document.write( "you confirm by substituting for x and y in each original expression of the rectangle to get:
\n" ); document.write( "AB = 5x = 5*7 = 35
\n" ); document.write( "BC = 5y = 5*4 = 20
\n" ); document.write( "CD = 7y + 7 = 7*4 + 7 = 28 + 7 = 35
\n" ); document.write( "AD = 2x + 6 = 2*7 + 6 = 14 + 6 = 20
\n" ); document.write( "we know that AB is supposed to be equal to CD and BC is supposed to be equal to AD.
\n" ); document.write( "we get:
\n" ); document.write( "35 = 35 for AB equal to CD and we get:
\n" ); document.write( "20 = 20 for BC equal to AD.
\n" ); document.write( "everything checks out so the values of x and y are good.
\n" ); document.write( " \n" ); document.write( "
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