Question 620108
Hi, there--
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STEP I: Choose variables
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Let W be the width of the rectangle.
Let L be the length.
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STEP II: Write equations to model the situation.
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The formula for the perimeter of a rectangle is P = 2W+2L, so 
{{{102=2W+2L}}}
{{{51=W+L}}}
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In algebra, "half as wide as it is long" can be written as 
{{{W=(1/2)*L}}} 
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Note: It's easy to confuse the words with the algebra. Once you have your equation test it with a few values. For example, "3 is half as wide as 6, and 3=(1/2)*6.
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STEP III: Solve your system of equations.
Substitute(1/2)*L for W in the first equation.
{{{51=W+L}}}
{{{51 = (1/2)*L+L}}}
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Simplify.
{{{51=(3/2)L}}}
{{{L=(2/3)(51)=34}}}
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The length of the rectangle is 34 inches.
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STEP IV: Check  your work.
Since the rectangle is half as wide as it is long, the width must be 17. Thus the perimeter is 2(17)+2(34)=34+68=102. Check!
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Hope this helps. Feel free to email if you still have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com