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?

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

RELATED QUESTIONS
The Johnson family is building a dog house. The total floor surface area will be 24 sq.... (answered by josmiceli,macston)

Jim built a rectangular shed with a total floor surface area will be 126 sq.ft if the... (answered by srinivas.g,MathTherapy)

hello if u can please help that would be great An architect is designing a house for... (answered by stanbon)

An architect is designing a house for the Frazier family. In the design he must consider... (answered by vleith)

Please help me with this math issue: Mr. and Mrs. Johnson have 3 children; a son... (answered by ankor@dixie-net.com)

The rectangular ground floor of the John Hancock building has a perimeter of 860 ft. The... (answered by ankor@dixie-net.com)

An architect is designing a house for the mullet family. In the design he must consider... (answered by Theo)

1. An architect is designing a house for the Frazier family. In the design, she must... (answered by ankor@dixie-net.com)

An office building has the following office spaces for lease. 1000 sq ft. or less... (answered by ewatrrr)