SOLUTION: We are stumped, I am trying to help my daughter and I have no clue help please.... The length of a rectangle is 1 inch more than twice its width. The value of the area of the r

Question 1018183: We are stumped, I am trying to help my daughter and I have no clue help please....
The length of a rectangle is 1 inch more than twice its width. The value of the area of the rectangle (in square inches) is 5 more than the value of the perimeter of the rectangle (in inches). find the width.
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You are given that

The perimeter of a rectangle is . Substituting for you get the perimeter as a function of the width:

The area of a rectangle is . Substituting for you get the area as a function of the width:

Since the value of the area is 5 greater than the perimeter, you can say:

which simplifies to:

Solve the factorable quadratic for the positive root. Then calculate .

John

My calculator said it, I believe it, that settles it

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
They are doing something a little bit illegal here
and you should be aware of it. They are saying
an area ( in square inches ) is equal to a perimeter
( in inches ).
You can only do this if you say the VALUES are equal,
but you can't make an equation and say
[ inches ] = [ square inches ]
--------------------------------
Let the length of the rectangle =
Let the width of the rectangle =
(1)
------------------
Let the area of the rectangle =
Let the perimeter of the rectangle =

and

----------------
They are saying:
( even though the units don't match )
(2)
Substitute (1) into (2)
(2)
(2)
(2)
(2)
Use the quadratic formula to solve

( note that I can't use the negative square root )
The width is 3.5 in
-----------------
check:
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
(2)
(2)
(2)
OK
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