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?

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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)   (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


Divide each side by 3
Subtract 8 sq ft from each side

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=36 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2, -4. Here's your graph:

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

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