SOLUTION: the�length�of�a�rectangle�Is�6�feet�more�than�three�times�the�width.�the�area�of�the�rectanle�is�240�square�feet.�what�are�the�dimensions?�

Question 216320: the�length�of�a�rectangle�Is�6�feet�more�than�three�times�the�width.�the�area�of�the�rectanle�is�240�square�feet.�what�are�the�dimensions?�
Found 2 solutions by drj, Earlsdon:
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The length of a rectangle is 6 feet more than three times the width. The area of the rectangle is 240 square feet. What are the dimensions?

Step 1. Let w be the width and 3w+6 is the length since rectangle is 6 feet more than three times the width.

Step 2. Area = width * length = w(3w+6) = 240 square feet

Step 3. Then we can put the equation in Step 2 in quadratic form

Subtract 240 to both sides of the equation

Step 4. We can use the quadratic formula given as

where a=3, b=6, and c=-240

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=2916 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8, -10. Here's your graph:

So select the positive solution for positive dimensions:

and

Verify area.... ...which is a true statement.

Step 5. Dimensions of the rectangle are a width of 8 feet and a length of 30 feet.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit
http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Area = L*W = 240
Substitute into the equation above:
Simplify.
Subtract 240 from both sides.
Factor a 3 just to simplify a bit.
so...
Factor the trinomial.
so that...
or which means that...
or Discard the negative solution as width can only be a positive value.
and

The length is 30 feet and the width is 8 feet.

RELATED QUESTIONS
what is the width of a rectanle with an area of 300 square feet and a length of l... (answered by jim_thompson5910)
What is the area, in square feet, of a rectangle whose width is 6 feet and whose length... (answered by macston)
The length of a rectangle is 6 feet more than three times the width. The perimeter is 36 (answered by checkley77)
the length of a rectangle is three feet more than twice the width . the area of the... (answered by mananth)
the perimeter of a rectangle is 52 feet. the length is 2 feet shorter than three times... (answered by Seutip)
The length of a rectangle is 6 feet less than 3 times its width. The area is 360 square... (answered by mananth)
The length of a rectangle is three feet more than twice the width. The area is 90... (answered by checkley79)
The area of a rectanle is 40. If the length is 6 more than the width, fidn the dimensions (answered by oscargut)
the perimeter of a rectangle is 36 feet. the length is 2 feet more than three times the... (answered by Hawksfan)