SOLUTION: the length of a rectangle is 6inch less than twice its width. If the perimeter of the rectangle is 72inches, find the dimesions of the rectangle. Please help use the simplest way t

Algebra ->  Rectangles -> SOLUTION: the length of a rectangle is 6inch less than twice its width. If the perimeter of the rectangle is 72inches, find the dimesions of the rectangle. Please help use the simplest way t      Log On


   

Question 571187: the length of a rectangle is 6inch less than twice its width. If the perimeter of the rectangle is 72inches, find the dimesions of the rectangle. Please help use the simplest way to solve this problem because I am not good in algebra and I know this has a little algebra in it.
Found 2 solutions by mrjunecarlo1095@ymail.com, Theo:
Answer by mrjunecarlo1095@ymail.com(10) About Me  (Show Source):
You can put this solution on YOUR website!
Let L be length: L = 2W-6
W be width : W = W
Perimeter is 72 inches.
Formula of Perimeter of a Rectangle: P=2L+2W
easily substitute L = 2W-6 to Length ,and W = W to Width
So, P= 2L+2W
by substitution P=72
72 = 2(2W-6) + 2W
72 = 4W - 12 +2W
72 + 12 = 6W
86 = 6W
so,
W= 14
and subs the value of W to L
L= 2W -6
= 2 (14) -6
= 28 - 6
= 22
Th answer is 22 by 14.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let L equal the length of your rectangle.
let W equal the width of your rectangle.
let P equal the perimeter of your rectangle.
the formula for the perimeter of a rectangle is 2L + 2W = P
since P equals 72, this formula becomes:
2L + 2W = 72
you are also given that L = 2W - 6
this equation says that the length of the rectangle is 6 inches less than twice the width.
you can substitute for L in the equation of:
2L + 2W = 72 to get:
2(2W-6) + 2W = 72
you simplify this equation to get:
4W - 12 + 2W = 72
you combine like terms to get:
6W - 12 = 72
you add 12 to both sides of this equation to get:
6W = 72 + 12
you combine like terms to get:
6W = 84
you divide both sides of this equation by 6 to get:
W = 84 / 6
you simplify this to get:
W = 14
since L = 2W - 6, this means that:
L = 2*14 - 6 which becomes:
L = 28 - 6 which becomes:
L = 22
you have:
L = 22 inches
W = 14 inches
going back to the original formula of:
2L + 2W = 72, you have:
2*22 + 2*14 = 72 which becomes:
44 + 28 = 72 which becomes:
72 = 72
this confirms the values for L and W are good.
your length is 22 inches.
your width is 14 inches.