SOLUTION: a community flower garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What ill be the

Question 503498: a community flower garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What ill be the width of the pathway?

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Borders are interesting because you have to remember that you have to pave the 4 corners.
.
The area of the garden = 12*16 = 192 square meters.
.
Then you add the border with width 'x'.
So,
Length is now L + 2x
Width is now W + 2x
.
We are told:
(L+2x)(W+2x) = 285
.
(12+2x)(16+2x) = 285
.
192 +24x +32x +4x^2 = 285
.
4x^2 + 56x + 192 = 285
.
4x^2 + 56x - 93 = 0
.

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=4624 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.5, -15.5. Here's your graph:

.
You cannot have a negative width, so the border is 1.5 m.
.
Always check your work.
L = 12 + 2(1.5) = 15
W = 16 + 2(1.5) = 19
15*19 = 285
Correct.
.
Answer: The border is 1.5 meters wide.
.
Done.
RELATED QUESTIONS
A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all... (answered by checkley77)

A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all... (answered by mananth)

a garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all... (answered by rapaljer)

A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed... (answered by scott8148)

A garden measuring 12 meters by 20 meters is to have a pedestrian pathway installed all... (answered by solver91311)

A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all... (answered by stanbon)

A garden measuring 12 meters by 16 meters is to have a pedestrain pathway installed all... (answered by mananth)

A gardening measuring 7 meters by 17 meters is to have a pedestrian pathway installed all (answered by Seutip)