document.write( "Question 1004416: The combined area of square and a rectangle is 57 square feet. The width of a rectangle is 3 feet more than the length of a side of the square, and the length of the rectangle is 5 feet more than the length of a side of the square. Find the length of the rectangle. \n" ); document.write( "
Algebra.Com's Answer #620924 by addingup(3677)\"\" \"About 
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Side of the square: x
\n" ); document.write( "Rectangle width and length:
\n" ); document.write( "width = 3 + x
\n" ); document.write( "length = 5 + x
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\n" ); document.write( "Area of square: x^2
\n" ); document.write( "area of rectangle: (3 + x)(5 + x)
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\n" ); document.write( "Add the area of the square and the rectangle:
\n" ); document.write( "x^2 + (3+x)(5+x) = 57 factor (FOIL) and you get:
\n" ); document.write( "x^2 + (15 + 8x + x^2) = 57 Add x^2 on left and subtract 15 on both sides:
\n" ); document.write( "2x^2 + 8x = 42 Divide both sides by 2:
\n" ); document.write( "x^2 + 4x= 21 Subtract 21 on both sides:
\n" ); document.write( "x^2 + 4x - 21 = 0 Factor this equation: you need to find factors of 21 that when added or subtracted will give you 4: 21 is divisible by 1, 3, 7, 21 We have our numbers, 7-3 = 4 and 7*-3= -21:
\n" ); document.write( "(x + 7)(x - 3) = 0 Split into 2 equations:
\n" ); document.write( "x+7= 0 or x-3= 0
\n" ); document.write( "x= -7 or x= 3 Eliminate -7 and you get:
\n" ); document.write( "x = 3 This is the side of the square
\n" ); document.write( "The rectangle:
\n" ); document.write( "Width: 3+3= 6
\n" ); document.write( "Length: 3+5= 8
\n" ); document.write( "Proof, Add areas:
\n" ); document.write( "Square: 3^2= 9
\n" ); document.write( "Rectangle: 6*8= 48
\n" ); document.write( "9+48= 57 We have the correct answer \n" ); document.write( "
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