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

Question 941014: The Johnson family is building a dog house. The total floor surface area will be 24 sq. ft. If the length is 6 more than three times the width what is the width of the dog house? I am very lost how do I get the width?
Found 2 solutions by josmiceli, macston:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
What they don't say is that the floor of
the dog house is a rectangle- but that's a
pretty safe assumption.
In a rectangle:
(1)
--------------
given:
ft2
(2) ft
---------------------
Substitute (2) into (1)
(1)
(1)
(1)
Divide both sides by
(1)
(1) ( by looking at it )
( can't use negative result )
and, since
(2)
(2)
(2)
---------------
The width is 2 ft
---------------
check:

OK

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
The floor area is 24 sq ft
Thus L x W = 24 sq ft
The length is 6 more then 3 times the width
L=3W+6 Substitute second equation in first for L
(3W+6) x W=24
Divide through by 3

subtract 8 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:

So W=2 or -4
For an actual measurement only the 2 makes sense
So W=2 feet L=3W+6=3(2)+6=6+6=12 feet
CHECK:
The area is 24 sq ft
A=L x W
24 sq ft=12 ft x 2 ft
24 sq ft=24 sq ft
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