SOLUTION: The dimensions of a rectangle are such that it's length is 3 inches more than it's width. If the length were doubled and if the width were decresed by 1 inch, the area would be 66i

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Question 632261: The dimensions of a rectangle are such that it's length is 3 inches more than it's width. If the length were doubled and if the width were decresed by 1 inch, the area would be 66inches squared. What are the length and width of the rectangle?
Thank you!
Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
l=w+3;
2l*(w-1)=66
l=8.08276, w=5.08276

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
it appears you needed the quadratic equation to solve this as it could not be factored because the roots are not integers.
using the quadratic equation, you get:
x1 = 5.08276253
x2 = -7.08276253
to find the solution and to be able to use the quadratic equation, you needed to do the following:
width of the rectangle is equal to x.
the length of the rectangle is equal to the width + 3 which make the length of the rectangle equal to x+3.
if you double the length, you get 2*(x+3) which is equal to 2x+6.
if you subtract 1 from the width, you get x-1.
after you've done this, the area is equal to 66 square inches.
since the area of a rectangle is equal to length times width, this means that:
(2x+6)*(x-1)=66
that's your equation and you have to solve for x.
simplify that equation to get:
2x^2-2x+6x-6=66
combine like terms to get:
2x^2+4x-6=66
subtract 66 from both sides of that equation to get:
2x^2+4x-72=0
divide both sides of that equation by 2 to get:
x^2+2x-36=0
since this doesn't factor, you need to use the quadratic formula
since this equation is in standard form, you get:
a=1
b=2
c=-36
use the quadratic formula to get:
x1 = 5.08276253
x2 = -7.08276253
since x2 is negative, it's not a good solution because the length of any side can't be negative.
this leaves x1 = 5.08276253 as your solution.
the length of your rectangle is equal to 2x+6 which is equal to 16.16552506.
the width of your rectangle is equal to x-1 which is equal to 4.08276253
area is equal to length times width which is equal to 16.16552506 * 4.08276253 which is equal to 66.
the quadratic formula is equal to:
x =