SOLUTION: The length of a rectangle is one foot less then three times the width. Find the length and width of the area is 30 square feet

Algebra ->  Expressions-with-variables -> SOLUTION: The length of a rectangle is one foot less then three times the width. Find the length and width of the area is 30 square feet      Log On


   

Question 447077: The length of a rectangle is one foot less then three times the width. Find the length and width of the area is 30 square feet
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let x ft be the width of the rectangle.
Let 3x-1 ft be the length of the rectangle.
...
l*w=A
(3x-1)(x)=30
3x^2-x=30
3x^2-x-30=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-1x%2B-30+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A3%2A-30=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+361+%29%29%2F2%5C3+=+3.33333333333333
x%5B2%5D+=+%28-%28-1%29-sqrt%28+361+%29%29%2F2%5C3+=+-3

Quadratic expression 3x%5E2%2B-1x%2B-30 can be factored:
3x%5E2%2B-1x%2B-30+=+3%28x-3.33333333333333%29%2A%28x--3%29
Again, the answer is: 3.33333333333333, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-1%2Ax%2B-30+%29

x must be positive.
x=3.33
3x-1=9
Therefore, the rectangle is 3.33 ft by 9 ft.