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perimeter with variables

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2 Answers

The perimeter of a rectangle is the distance completely around the rectangle.  Imagine you're walking around the rectangle starting from a corner.  You'd walk up the length L, then turn and walk along the width W, then turn and walk another length L, then turn and walk another width W to get back to where you started.  So you walked 2 lengths and 2 widths,  The perimeter then is computed as:
 
Perimeter of a rectangle = 2L + 2W = 2(L + W)
 
In your problem, the perimeter is 64 feet and the width is 1/2 the length minus one foot, which is W = (1/2)L - 1.  Looks like you almost got it right.  Now plug (1/2)L-1 in for W in the Perimeter equation above and let me know what you get (in the comments).
 
[Teaching moment.  Please let the student complete the solution.  Thank you.]

Comments

Karen;
He wants you to complete the solution.
Let's see if our answers match.
Hi Karen;
length....x
width...(1/2)x-1
perimeter=64
 
perimeter=2(length+width)
64=2[x+(1/2)x-1]
64=2[(3/2)x-1]
64=3x-2
Add 2 to both sides...
64+2=3x-2+2
66=3x
Divide both sides by 3...
66/3=(3x)/3
22=x
 
length...22
width...[(1/2)(22)]-1=11-1=10
 
Let's check our work...
perimeter=2(length+width)
 
64=2(22+10)
64=2(32)
64=64