document.write( "Question 552071: A wire is first bent into the shape of a rectangle with width and length . Then the wire is unbent and reshaped into a triangle. If each side of the triangle has equal length, what is this length? \n" ); document.write( "
Algebra.Com's Answer #360109 by Theo(13342)\"\" \"About 
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the length of the wire is set equal to z.
\n" ); document.write( "the width of the rectangle is set equal to x.
\n" ); document.write( "the length of the rectangle is set equal to y.
\n" ); document.write( "the perimeter of the rectangle is equal to z.
\n" ); document.write( "the perimeter of the rectangle is also equal to 2x + 2y.
\n" ); document.write( "this results in:
\n" ); document.write( "2x + 2y = z
\n" ); document.write( "since z is the perimeter of the triangle also, then each side of the equilateral triangle is equal to z/3.
\n" ); document.write( "you have one equation in 3 unknowns which means that:
\n" ); document.write( "if you know the value of 2 of the unknowns, you can solve for the third value.
\n" ); document.write( "other than that, all you have is a relationship that will not yield a specific value unless you know 2 of the other values.
\n" ); document.write( "suppose we know that:
\n" ); document.write( "x = 5 and z = 60
\n" ); document.write( "we'll use the equation of 2x + 2y = z to get:
\n" ); document.write( "2(5) + 2y = 60
\n" ); document.write( "simplify this to get:
\n" ); document.write( "10 + 2y = 60
\n" ); document.write( "subtract 10 from both sides of this equation to get:
\n" ); document.write( "2y = 50
\n" ); document.write( "divide both sides of this equation by 2 to get:
\n" ); document.write( "y = 25
\n" ); document.write( "we now have:
\n" ); document.write( "x = 5 (given)
\n" ); document.write( "y = 25 (solved for)
\n" ); document.write( "z = 60 (given)
\n" ); document.write( "the dimensions of the rectangle are:
\n" ); document.write( "length = 5 and width = 25
\n" ); document.write( "the perimeter of the rectangle is equal to 2*5 + 2*25 which is equal to 60 which is the value of z.
\n" ); document.write( "the same value of z is also the perimeter of the triangle.
\n" ); document.write( "the length of each side of the triangle is set equal to k.
\n" ); document.write( "since the triangle is equilateral, then the length of each side of the triangle is equal to z/3 which makes k = z/3 which makes k equal to 60/3 which is equal to 20.
\n" ); document.write( "you have:.
\n" ); document.write( "the length of the rectangle is equal to x which is equal to 5
\n" ); document.write( "the width of the rectangle is equal to y which is equal to 25
\n" ); document.write( "the length of each side of the triangle is equal to k which is equal to 20.
\n" ); document.write( "the relationship between these is:
\n" ); document.write( "2x + 2y = 3k
\n" ); document.write( "this stems from 2*x + 2*y = z where z is equal to 3 * k where k is the length of each side of the triangle.
\n" ); document.write( "the equation of:
\n" ); document.write( "2x + 2y = z becomes:
\n" ); document.write( "2x + 2y = 3k
\n" ); document.write( "if you know 2 of the values, you can solve for the third.
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