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, increasi

Question

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

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Kaylee 2 weeks 2021-11-20T19:45:25+00:00 1 Answer 0

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    2021-11-20T19:46:56+00:00

    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)=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

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