SOLUTION: the length of a rectangle is 4 feet less than twice its width. If the area of the rectangle is 240 square feet then its dimensions are:

Algebra ->  Rectangles -> SOLUTION: the length of a rectangle is 4 feet less than twice its width. If the area of the rectangle is 240 square feet then its dimensions are:      Log On


   

Question 765592: the length of a rectangle is 4 feet less than twice its width. If the area of the rectangle is 240 square feet then its dimensions are:
Answer by 2897696(96) About Me  (Show Source):
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First make variables for both dimensions
let x=width
length= 2x-4
since finding area is L*W plug in the variables of the dimensions
so:
(2x-4)x=240 ==> 2x^2-4x=240
now put the equation into quadratic form
so:
2x^2-2x-240=0 from here factor and find value of x
factoring: 2(x^2-2x-120)* I undistributed 2
factor x^2-2x-120=0 ==> (x-12) (x+10)
now put all the factors together:
2(x-12)(x+10)=0 solve for x by putting each group of numbers to 0
2=0 x-12=0 x+10=x
2=0 is not a solution because, 2 does NOT EQUAL zero
x+10=0 ==> x=-10
this is not a solution because there is no such thing as a negative length
however:
x-12=0 ==> x=12
is the solution because 12 is the only possible solution
now that we have found the width, plug in the values to find length which is
2x-4 ==> 2(12)-4 ==> 24-4 ==>20 so the length is 20
ANSWER:
so the solutions are 12ft and 20ft