SOLUTION: The perimeter of a rectangle is 38 inches, and its area is 88 in2. Find the length of the longer and shorter side.

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Question 595488: The perimeter of a rectangle is 38 inches, and its area is 88 in2. Find the length of the longer and shorter side.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
.
We can solve this problem using a system of equations.
.
[I]Define your variables.
L = the longer side
S = the shorter side
.
[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.
.
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%2B2L=38
.
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
%28S%29%28L%29=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%2B2L=38
2S=38-2L
S=%2838-2L%29%2F2
S=19-L
.
Substitute 19-L for S in the second equation.
%28S%29%28L%29=88
%2819-L%29%28L%29=88
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Simplify (you'll get a quadratic equation) and solve for L.
19L-L%5E2=88
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Rearrange the equation and set it equal to 0.
-L%5E2%2B19L-88=0
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Multiply every term by -1.
L%5E2-19L%2B88=0
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This equation factors nicely since (-11)(-8)=88 and (-11)+(-8)=-19.
.
%28L-11%29%28L-8%29=0%29
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We use the zero-product property to say that either
L-11=0
or
L-8=0
.
Therefore,
L=11
or
L=8
.
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.
.
[IV] Check your work checking the perimeter and area for these values!
Perimeter:
2L%2B2S=38
2%2811%29%2B2%288%29=38
22%2B16=38
38=38
Perfect!
.
Area:
%28S%29%28L%29=88
%288%29%2811%29=88
88=88
Winner, winner, chicken dinner!
.
That's it. Feel free to email me if you have questions about the solution.
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Good luck,
.
Mrs.Figgy
math.in.the.vortex@gmail.com