find the width of the pathway if a garden measuring 15 meters by 18 meters is to have a pedestrian pathway installed all around it, increasing the total area to 360 square meters

1.2664 meters.

Step-by-step explanation:

Let x be the width of the walkway that will surround the garden. There are three rectangles to focus; the larger rectangle, the garden itself, and the rectangle that represents the walkway around the garden. Our equation will include the area of all three rectangles.

Length including pathway = 18+x+x = 18 + 2x

width including pathway = 15+x+x = 15+2x

(18+2x) (15+2x) = 360

Or, 270+36x+30x+4x^2=360

Or, 4x^2+66x+270-360=0

Or, 4x^2+66x-90=0

Solving this equation we get, x = 1.2664 and x = - 17.7664.

x = - 17.7664 is unacceptable because width cannot be negative. So, the value of x is 1.2664.

Proof: Now we put the value of x in the equation. If left hand side and right hand side are equal then the answer is right.

Or, (18+2*1.2664) (15+2*1.2664) = 360

Or, (18+2.5328) (15+2.5328) = 360

Or, 20.5328*17.5328=360

Or, 360=360