SOLUTION: Problem: Originally, a rectangle was three times as long as it is wide. When 2 cm were subtracted from the length and 5 cm were added to the width, the resulting rectangle had an a

Question 251684: Problem: Originally, a rectangle was three times as long as it is wide. When 2 cm were subtracted from the length and 5 cm were added to the width, the resulting rectangle had an area of 90 cm squared. Find the dimensions of the new rectangle.
hmmmm, I tried this problem...but I keep getting decimal answers when solving :/ We are supposed to use only one variable in the actual equation, and use Quadratic equations to solve.
My Attempt:
w=width
l=length
l=3w
Formula-
A=width(length)
(3w-2)(w+5)=90
Then I foiled and got:
3w^2+13w-100=0
And I get stuck there :/ I don't think it factors and I'm not sure if I foiled wrong or set it up wrong. :/ Help me, please? Thanks :)
I put this under Algebra, although I am in Algebra II, I hope that is fine :D
Found 2 solutions by jsmallt9, richwmiller:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Then I foiled and got:

And I get stuck there :/ I don't think it factors and I'm not sure if I foiled wrong or set it up wrong. :/ Help me, please? Thanks :)
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This is all good. If you think this trinomial does not factor, then use the quadratic formula on it. (This trinomial actually does factor but the quadratic formula still works.)

Your a = 3, b = 13 and c = -100:

or
or
or
Since w represents the side of a rectangle we will reject the negative solution. So the only possible value for w that works is w = 4. And that makes the original length, which is 3w, 12.

BTW: factors into:

And this gives us the same answers as the quadratic formula did.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
so far so good
It factors to
(w-4)(3w+25) = 0
which yields two answers 4 and -25/3
We need a positive answer.
notice that below that even factored out the 3
and got 3*(w-4)*(w+8.33)
so 3w^2+13w-100=3*(w^2+4 1/3 w-33 1/3)which factors into 3*(w-4)*(w+8 1/3)
You could also have used the quadratic formula. See below
which would have been the best choice after not finding factors.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1369 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, -8.33333333333333. Here's your graph:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=152.111111111111 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, -8.33333333333333. Here's your graph:

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