document.write( "Question 1160800: A square has its length increased by 6 feet and its width by 8 feet. If the resulting rectangle has an area of 239.25 square feet what was the perimeter of the original square? \n" ); document.write( "

Algebra.Com's Answer #784197 by Theo(13342) $\"\"$ $\"About$

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s = length of a side of a square.
\n" ); document.write( "area of square = S^2.
\n" ); document.write( "perimeter of square = 4*S.
\n" ); document.write( "L = length of a rectangle.
\n" ); document.write( "W = width of a rectangle.
\n" ); document.write( "add 6 feet to the length of the square and 8 feet to the width of the square and you get a rectangle that has L = S + 6 and W = S + 8.
\n" ); document.write( "you are given that the area of the rectangle is 239.25 square feet.
\n" ); document.write( "that means that (S + 6) * (S + 8) = 239.25
\n" ); document.write( "simplify this and subtract 239.25 from both sides of the equation and combine like terms and order the terms in descending order of degree and you get:
\n" ); document.write( "S^2 + 14*S - 191.25 = 0
\n" ); document.write( "factor this quadratic equation to get:
\n" ); document.write( "S = -22.5 or 8.5
\n" ); document.write( "S can't be negative, so S must be equal to 8.5.
\n" ); document.write( "the area of the rectangle would be (8.5 + 6) * (8.5 + 8) = 239.25 square feet, so that checks out ok.
\n" ); document.write( "the perimeter of the square would then be 4 * 8.5 = 34 feet.
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