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)   (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

.
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

.
[III] Solve the system of equations.
Let's use the substitution method. Rewrite the first equation to isolate S.




.
Substitute 19-L for S in the second equation.


.
Simplify (you'll get a quadratic equation) and solve for L.

.
Rearrange the equation and set it equal to 0.

.
Multiply every term by -1.

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This equation factors nicely since (-11)(-8)=88 and (-11)+(-8)=-19.
.

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We use the zero-product property to say that either

or

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Therefore,

or

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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:




Perfect!
.
Area:



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,
.
Mrs.Figgy
math.in.the.vortex@gmail.com




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