document.write( "Question 101538: An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m^2. Find the dimensions of the garden. \n" ); document.write( "

Algebra.Com's Answer #73917 by Earlsdon(6294) $\"\"$ $\"About$

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Start with the basic formulas for perimeter and area:
\n" ); document.write( "1) P = 2(L+W) where L = Length and W = Width.
\n" ); document.write( "2) A = L*W
\n" ); document.write( "You are given that P = 300m and A = 5000 sq.m. so plug these values into the two equations thus:
\n" ); document.write( "1a) 300 = 2(L+W)
\n" ); document.write( "2a) 5000 = L*W
\n" ); document.write( "Now you have a system of equations with two unknowns.
\n" ); document.write( "Solve equation 1a) for L
\n" ); document.write( "1b) L = 150-W now substitute this into equation 2a) and solve for W.
\n" ); document.write( "2b) 5000 = (150-W)*W Simplify this.
\n" ); document.write( "W^2-150W+5000 = 0 This quadratic equation can be solved by factoring, so...
\n" ); document.write( "(W-100)(W-50) = 0
\n" ); document.write( "So W = 100 or W = 50
\n" ); document.write( "Now we need to find L and we can use equation 1b.
\n" ); document.write( "L = 150 - W and, if W = 50m, then:
\n" ); document.write( "L = 100m or, if W = 100m, then:
\n" ); document.write( "L = 50m.
\n" ); document.write( "The dimensions of the garden are: 100m by 50m
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