You can
put this solution on YOUR website! A rectangular flower bed 30 yards long by 20 yards wide has a walk of uniform width around it. If the area of the path is 1/4 that of the flower bed, find the width of the path.
.
Let w = width of path
then
Area of flower bed = (30)(20) = 600 sq yards
.
Area of flower bed and walk = (30+2w)(20+2w)
.
Area of path = "area of flower bed and walk" - "area of flower bed"
Area of path = (30+2w)(20+2w) - 600
.
(1/4)600 = (30+2w)(20+2w) - 600
150 = (30+2w)(20+2w) - 600
750 = (30+2w)(20+2w)
750 = 600+60w+40w+4w^2
750 = 4w^2+100w+600
0 = 4w^2+100w-150
0 = 2w^2+50w-75
Using the quadratic equation we get:
w = {1.42, -26.42}
Throw out the negative solution leaves us with:
w = 1.42 yards
.
Details of quadratic to follow:
| 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=3100 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 1.41941090707505, -26.4194109070751.
Here's your graph:
 |
