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

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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) About Me  (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) +A+=+L%2AW+
--------------
given:
+A+=+24+ ft2
(2) +L+=+3W+%2B+6+ ft
---------------------
Substitute (2) into (1)
(1) +24+=+%28+3W+%2B+6+%29%2AW+
(1) +24+=+3W%5E2+%2B+6W+
(1) +3W%5E2+%2B+6W+-+24+=+0+
Divide both sides by +3+
(1) +W%5E2+%2B+2W++-+8+=+0+
(1) +%28+W+%2B+4+%29%2A%28+W+-+2+%29+=+0+ ( by looking at it )
+W+=+2+ ( can't use negative result )
and, since
(2) +L+=+3W+%2B+6+
(2) +L+=+3%2A2+%2B+6+
(2) +L+=+12+
---------------
The width is 2 ft
---------------
check:
+A+=+W%2AL+
+24+=+2%2A12+
+24+=+24+
OK

Answer by macston(5194) About Me  (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
3w%5E2+%2B+6W=24 Divide through by 3
%283W%5E2%2B6W%29%2F3=24%2F3
W%5E2%2B2W=8 subtract 8 from each side
W%5E2%2B2W-8=8-8
w%5E2%2B2W-8=0
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

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