perimeter with variables

Question

the perimeter of a rectangle is 64f  the width is 1/2 the length less 1 foot shouldnt the equation be 

1+1/2l- 1 equals 64

Answer 1

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.]

Answer 2

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