SOLUTION: The Johnson family is building a dog house. The total floor-surface are will be 24sq. ft if the length is 6 more than three times the width, what is the width of the dog house?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The Johnson family is building a dog house. The total floor-surface are will be 24sq. ft if the length is 6 more than three times the width, what is the width of the dog house?      Log On


   

Question 949244: The Johnson family is building a dog house. The total floor-surface are will be 24sq. ft if the length is 6 more than three times the width, what is the width of the dog house?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
W=width; L=length=3W+6; A=L*W=24 sq ft
A=L*W Substitute for L
24+sq+ft=%283W%2B6%29%2AW
24+sq+ft=3W%5E2%2B6W+
24+sq+ft=3%28W%5E2%2B2W%29 Divide each side by 3
8+sq+ft=W%5E2%2B2W Subtract 8 sq ft from each side
0=W%5E2%2B2W-8+sq+ft
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 1W%5E2%2B2W%2B-8+=+0) has the following solutons:

W%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=%282%29%5E2-4%2A1%2A-8=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+36+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%282%29%2Bsqrt%28+36+%29%29%2F2%5C1+=+2
W%5B2%5D+=+%28-%282%29-sqrt%28+36+%29%29%2F2%5C1+=+-4

Quadratic expression 1W%5E2%2B2W%2B-8 can be factored:
1W%5E2%2B2W%2B-8+=+1%28W-2%29%2A%28W--4%29
Again, the answer is: 2, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-8+%29

Here we need the positive answer, so ANSWER 1: The width is 2 feet.
L=3W+6 feet=3(2 feet)+6 feet=6 feet+6 feet=12 feet ANSWER 2: the length is 12 feet
CHECK:
Area is 24 sq ft
24 sq ft=L*W
24 sq ft=12 feet*2 feet
24 sq ft=24 sq ft