Question 595488
Hi, there--
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We can solve this problem using a system of equations.
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[I]Define your variables.
L = the longer side
S = the shorter side

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[II] Write the system of equations.
We will need to use the formulas for the perimeter of a rectangle and for the area of a rectangle to write our equations. 
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The PERIMETER is the distance around the edge of the rectangle, so an algebraic expression for the perimeter is S+L+S+L. We can simplify this to 2S+2L. Since the perimeter is 38 inches, our first equation is 
{{{2S+2L=38}}}
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The AREA is the space inside the rectangle, so an algebraic expression for the area is (S)(L). Since the area is 88 square inches, our second equation is 
{{{(S)(L)=88}}}
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[III] Solve the system of equations.
Let's use the substitution method. Rewrite the first equation to isolate S.
{{{2S+2L=38}}}
{{{2S=38-2L}}}
{{{S=(38-2L)/2}}}
{{{S=19-L}}}
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Substitute 19-L for S in the second equation.
{{{(S)(L)=88}}}
{{{(19-L)(L)=88}}}
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Simplify (you'll get a quadratic equation) and solve for L.
{{{19L-L^2=88}}}
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Rearrange the equation and set it equal to 0.
{{{-L^2+19L-88=0}}}
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Multiply every term by -1.
{{{L^2-19L+88=0}}}
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This equation factors nicely since (-11)(-8)=88 and (-11)+(-8)=-19.
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{{{(L-11)(L-8)=0)}}}
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We use the zero-product property to say that either
{{{L-11=0}}}
or
{{{L-8=0}}}
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Therefore,
{{{L=11}}}
or 
{{{L=8}}}
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Either the longer side is 11 inches or 8 inches. Clearly the longer side L is 11 inches since 11 is greater than 8. The shorter side S is 8 inches.
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[IV] Check your work checking the perimeter and area for these values!
Perimeter:
{{{2L+2S=38}}}
{{{2(11)+2(8)=38}}}
{{{22+16=38}}}
{{{38=38}}}
Perfect!
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Area:
{{{(S)(L)=88}}}
{{{(8)(11)=88}}}
{{{88=88}}}
Winner, winner, chicken dinner!
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That's it. Feel free to email me if you have questions about the solution.
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Good luck,
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Mrs.Figgy
math.in.the.vortex@gmail.com