SOLUTION: Please help me solve this problem: A rectangular pond measures 3m by 5m. A concrete walk of uniform width is constructed around the pond. If the walk and pond together cove

Question 168386: Please help me solve this problem:
A rectangular pond measures 3m by 5m. A concrete walk of uniform width is constructed around the pond. If the walk and pond together cover an area of 39m^2, how wide is the walk?
Found 2 solutions by checkley77, nerdybill:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
3*5=15 M^2 FOR THE POND.
(3+2X)(5+2X)=39
15+10X+6X+4X^2-39=0
4X^2+16X-24=0
4(X^2+4X-6)=0
USING THE QUADRATIC EQUATIONWE GET:
X=(-4+-SQRT[4^2-4*1*-6])/2*1
X=(-4+-SQRT16+24])/2
X=(-4+-SQRT40)/2
X=(-4+-6.325)/2
X=(-4+6.32)/2
X=2.32/2
X=1.16 M. IS THE WIDTH OF THE WALK.
PROOF:
(3+2*1.16)(5+2*1.16)=39
(3*2.32)(5+2.32)=39
5.32*7.32=39
39~39

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A rectangular pond measures 3m by 5m. A concrete walk of uniform width is constructed around the pond. If the walk and pond together cover an area of 39m^2, how wide is the walk?
.
Let w = width of walk
.
width of pond w/walk = 3+2w
length of pond w/walk = 5+2w
.
39 = (3+2w)(5+2w)
39 = 15 + 6w + 10w + 4w^2
39 = 15 + 16w + 4w^2
0 = -24 + 16w + 4w^2
0 = 4w^2 + 16w - 24
0 = w^2 + 4w - 6
.
Using the quadratic equation to solve we get:
x = {1.162, -5.162}
.
We can toss out the negative answer leaving us with:
1.162 meters (width of walk)
.
Here's the details of the quadratic:

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=40 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.16227766016838, -5.16227766016838. Here's your graph:

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