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

Answer: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)=360Or, 270+36x+30x+4x^2=360Or, 4x^2+66x+270-360=0Or, 4x^2+66x-90=0Solving 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)=360Or, (18+2.5328)(15+2.5328)=360Or, 20.5328*17.5328=360Or, 360=360