SOLUTION: A rectangle is 4 times as long as it is wide. The area is 144 square feet. What is the perimeter of the rectangle?

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Question 903448: A rectangle is 4 times as long as it is wide. The area is 144 square feet. What is the perimeter of the rectangle?
Found 2 solutions by ewatrrr, Stitch:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

     .

x the width

(4w)w = 144ft^2

 w^2 = 36 (Tossing out the negative solution for unit measure)

 w = 6ft and L = 24ft

P = 12ft + 48ft = 60ft

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Let L = the length of the rectangle
Let W = the Width of the rectangle
The equation for the Area of a rectangle is A = L x W
The equation for the perimeter of a rectangle is P = 2L + 2W
-----------------------
Equation 1: 144+=+L+%2A+W
Equation 2: L+=+4W (The rectangle is 4 times as long as it is wide)
Equation 3: P+=+2L+%2B+2W
Note that equation 2 is already solved for L.
Plug (4W) into equation 1 for L
Equation 1: 144+=+L+%2A+W
144+=+%284W%29+%2A+W
Combine like terms
144+=+4W%5E2
Divide both sides by 4
36+=+W%5E2
Take the square root of both sides
sqrt%2836%29+=+sqrt%28W%5E2%29
highlight%286+=+W%29
-----------------------
Now plug 6 into equation 2 for W
Equation 2: L+=+4W
L+=+4%2A%286%29
highlight_green%28L+=+24%29
-----------------------
Now Plug L=24, and W=6 into equation 3
Equation 3: P+=+2L+%2B+2W
P+=+2%2A%2824%29+%2B+2%2A%286%29
Simplify
P+=+48+%2B+12
highlight%28P+=+60%29
The perimeter is 60ft