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

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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