SOLUTION: the length of a rectangular picture is 4 less than twice its width. it is placed in a wooden frame with a unifiorm width of 2 inches. The perimeter of the picture frame is 102 inch

Algebra ->  Rectangles -> SOLUTION: the length of a rectangular picture is 4 less than twice its width. it is placed in a wooden frame with a unifiorm width of 2 inches. The perimeter of the picture frame is 102 inch      Log On


   

Question 257662: the length of a rectangular picture is 4 less than twice its width. it is placed in a wooden frame with a unifiorm width of 2 inches. The perimeter of the picture frame is 102 inches. what is the dimension of the rectangular picture?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the length of a rectangular picture is 4 less than twice its width.
it is placed in a wooden frame with a uniform width of 2 inches.
The perimeter of the picture frame is 102 inches.
what is the dimension of the rectangular picture?
:
Let x = the width
it states:"the length of a rectangular picture is 4 less than twice its width."
Therefore:
L = (2x - 4)
:
Perimeter
2L + 2x = 102
Simplify, divide by 2
L + x = 51
Replace L with (2x-4), find x:
2x - 4 + x = 51
3x = 51 + 4
3x = 55
x = 55/3
x = 181%2F3 inches is the frame width
then
L = 2(181%2F3) - 4
L = 362%2F3 - 4
:
L = 322%2F3 inches is the frame length
:
A picture frame with 2 inches width all around, subtract 4 inches
therefore
181%2F3 - 4 = 141%2F3 picture width
:
322%2F3 - 4 = 282%2F3 picture length
:
:
Note to students response.
Actually I think you have to subtract 16" from the frame perimeter to get the picture perimeter.
Then the picture length and width will agree. (86")