document.write( "Question 118245: a>
\n" ); document.write( "Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its lenght and breadth.\r
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\n" ); document.write( "The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Determine their present ages.\r
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\n" ); document.write( "Is it possible to design a rectangular park of perimeter 80 m and 400 m2? If so, find its lenght and breadth.\r
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Algebra.Com's Answer #86343 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Is it possible to design a rectangular mango grove whose length is twice it's breadth, and the area is 800 m2? If so, find its length and breadth.
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\n" ); document.write( "It's possible.
\n" ); document.write( "Let x = width of the grove
\n" ); document.write( "Then
\n" ); document.write( "2x = length
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\n" ); document.write( "Area = L * W:
\n" ); document.write( "x(2x) = 800
\n" ); document.write( "2x^2 = 800
\n" ); document.write( "x^2 = 800/2
\n" ); document.write( "x^2 = 400
\n" ); document.write( "x = Sqrt(400)
\n" ); document.write( "x = 20 m by 40 m
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\n" ); document.write( "b>
\n" ); document.write( "The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Determine their present ages.
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\n" ); document.write( "It would simply things if we let x and y be the ages 4 years ago
\n" ); document.write( "Then
\n" ); document.write( "(x+4) and (y+4) = ages now
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\n" ); document.write( "Present age sum = 20:
\n" ); document.write( "(x+4) + (y+4) = 20
\n" ); document.write( "x + y + 8 = 20
\n" ); document.write( "x + y = 20 - 8
\n" ); document.write( "x + y = 12
\n" ); document.write( "y = 12-x
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\n" ); document.write( "Product of age 4 yrs ago
\n" ); document.write( "x*y = 48
\n" ); document.write( "y = 48/x
\n" ); document.write( "Replace y with 12-x
\n" ); document.write( "12-x = 48/x
\n" ); document.write( "12x - x^2 = 48
\n" ); document.write( "-x^2 + 12x - 48 = 0
\n" ); document.write( "This equation has no real roots, (discriminant less than 0)
\n" ); document.write( "There is no solution
\n" ); document.write( "If we plot these equations, you can see they don't intersect
\n" ); document.write( "y = 12-x and y = 48/x
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\n" ); document.write( "\"+graph%28+300%2C+200%2C+-2%2C+10%2C+-2%2C+20%2C+12-x%2C+48%2Fx%29+\"
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\n" ); document.write( "c>
\n" ); document.write( "Is it possible to design a rectangular park of perimeter 80 m and 400 m2? If so, find its length and breadth.
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\n" ); document.write( "It is: let the sides = x and y
\n" ); document.write( "Perimeter: 2x + 2y = 80
\n" ); document.write( "Simplify, divide by 2
\n" ); document.write( "x + y = 40
\n" ); document.write( "y = (40-x)
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\n" ); document.write( "Area:
\n" ); document.write( "x * y = 400
\n" ); document.write( "Replace y with (40-x)
\n" ); document.write( "x(40-x) = 400
\n" ); document.write( "40x - x^2 = 400
\n" ); document.write( "-x^2 + 40x - 400 = 0
\n" ); document.write( "Easier to factor if we multiply by -1
\n" ); document.write( "x^2 - 40x + 400 = 0
\n" ); document.write( "Factor
\n" ); document.write( "(x-20)(x-20) = 0
\n" ); document.write( "x = 20,
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\n" ); document.write( "The park will be a square; 20 by 20\r
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