Please help with this problem.....I know the answer, but I don't understand how, please show work.?

Question

The length of a rectangle is 1 inch less than twice the width. The area of the rectangle is 91 in^2. Find the length of the rectangle......Answer is 13 in

Answer 1

Let's say the width is w.
Then the length is 2w - 1
The area is length times width so
w(2w - 1) = 91
This is a quadratic equation, so put it in standard form...
2w^2 - w - 91 = 0
From here you could put it in the quadratic formula or factor, as others have shown. Be careful; the result will be w, the width, and you are looking for the length so you'll have to convert, that is, multiply it by 2 and take away 1 like the problem says.
Or you could have used the given info as a clue, think about factors of 91, 91 = 7 x 13. 7, the lesser number, is the width.
The lenth is 2x7 - 1 = 13
For more info on how to do these see
http://www.purplemath.com/modules/translat.htm
http://www.purplemath.com/modules/perimetr.htm
see also
http://www.purplemath.com/modules/why_math.htm

Answer 2

Just set the problem up the way the problem tells you to. Call the width of the rectangle w. What does the problem say? The length is 1 inch less than twice the width. l = 2w-1. Now you know that the area is length times width, so
A = l * w = (2w-1)*w = 2w² - w = 91 (the problem told you that area was 91 in²) Now you have an equation
2w² - w = 91 which becomes
2w² - w - 91 = 0 which is a quadratic and has 2 answers, 13 and 7 (which are the length and width of the rectangle)

Doug

Answer 3

Width = w
Length = l = 2w-1

Area = lw = (2w-1)w = 91

2w^2 - w - 91 = 0
2w^2 - 14w + 13w - 91 = 0
2w(w-7) + 13(w-7) = 0
(w-7)(2w+13) = 0
w = -13 ---- ignore this answer (width cannot be negative)
w = 7

l = 2w - 1
= 2*7 - 1
= 13 in

Answer 4

let x = the width
let 2x-1 = the length

x(2x-1) = 91
2x^2 - x = 91
subtract 91 from both sides
---------------------
2x^2-x-91 = 0
(x-7)(2x+13)=0
x=7 2x=-13 (this is extraneous because a length cant be negative)

then you plug x into the statement in the beginning...
let 2x-1 = the length
2(7)-1 = 13
therefore, the length is 13

Answer 5

Let x = width
2x-1 = length
Area=x(2x-1)=91
2x^2-x-91=0
(2x+13)(x-7)=0
x=-13/2 (reject) x=7
length = 2(7)-1 = 13