SOLUTION: Hello I need help with my homework. Can you please explain how to solve this word problem The length of a rectangle is 3 m less than twice the width, and the area of the

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello I need help with my homework. Can you please explain how to solve this word problem The length of a rectangle is 3 m less than twice the width, and the area of the      Log On


   

Question 961525: Hello I need help with my homework. Can you please explain how to solve this word problem
The length of a rectangle is

3 m
less than twice the width, and the area of the rectangle is

65 m^2
. Find the dimensions of the rectangle.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let the length of a rectangle be L and the width W

if L is 3m less than twice the width W,we have
L=2W-3m

and if the area A of the rectangle is A=65m%5E2, then
L%2AW=65m%5E2....substitute 2W-3m for L
%282W-3m%29%2AW=65m%5E2.............solve for W
%282W%5E2-3Wm%29=65m%5E2
2W%5E2-3Wm-65m%5E2=0

W+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
W+=+%28-%28-3m%29+%2B-+sqrt%28+%28-3m%29%5E2-4%2A2%2A%28-65m%5E2%29+%29%29%2F%282%2A2%29+
W+=+%283m+%2B-+sqrt%28+9m%5E2%2B520m%5E2+%29%29%2F4+
W+=+%283m+%2B-+sqrt%28+529m%5E2+%29%29%2F4+
W+=+%283m+%2B-+23m%29%2F4+.......since this is a width, we need only positive solution
W+=+%283m+%2B+23m%29%2F4+
W+=+26m%2F4+
highlight%28W+=+6.5m%29+
now find the length
L=2W-3m
L=2%2A6.5m-3m
L=13m-3m
highlight%28L=10m%29