SOLUTION: How do you find the answer to this word problem: The perimeter of a rectangular garden is 40ft. The width is 2ft. more than one-half the length. Find the length and width.

Algebra ->  Equations -> SOLUTION: How do you find the answer to this word problem: The perimeter of a rectangular garden is 40ft. The width is 2ft. more than one-half the length. Find the length and width.       Log On


   

Question 37922: How do you find the answer to this word problem:

The perimeter of a rectangular garden is 40ft. The width is 2ft. more than one-half the length. Find the length and width.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the perimeter of a rectangle:
P+=+2L%2B2W
In your problem, P = 40ft.
W+=+L%2F2+%2B+2
L+=+L
Substitute these into the basic formula above:
40+=+2L+%2B+2%28L%2F2+%2B+2%29 Simplify and solve for L
40+=+2L+%2B+L+%2B+4
40+=+3L+%2B+4 Subtract 4 from both sides of the equation.
36+=+3L Divide both sides by 3.
12+=+L
The length is 12ft.
The width isL%2F2%2B2+=+12%2F2+%2B+2 = 8ft.
Check:
P+=+2L%2B2W
P+=+2%2812%29%2B2%288%29
P+=+24%2B16
P+=+40 It checks!