Respuesta :
x= width of the path.
we can suggest this equation:
(20+2x)(28+2x)=1584
we solve this equation:
(20+2x)(28+2x)=1584
560+40x+56x+4x²=1584
4x²+96x-1024=0
4/4x²+96/4x-1024/4=0/4
x²+24x-256=0
We solve this square equation:
x=[-24⁺₋√(576+1024)]/2=(-24⁺₋40)/2
we have two solutions:
x₁=(-24-40)/2=-32 this solution is not valid.
x₂=(-24+40)/2=8
Answer: the width of the path is 8 m.
we can suggest this equation:
(20+2x)(28+2x)=1584
we solve this equation:
(20+2x)(28+2x)=1584
560+40x+56x+4x²=1584
4x²+96x-1024=0
4/4x²+96/4x-1024/4=0/4
x²+24x-256=0
We solve this square equation:
x=[-24⁺₋√(576+1024)]/2=(-24⁺₋40)/2
we have two solutions:
x₁=(-24-40)/2=-32 this solution is not valid.
x₂=(-24+40)/2=8
Answer: the width of the path is 8 m.
The width of the path is 16 meters.
How to find the area of a rectangle?
The area of a rectangle can be found by multiplying the length and width of the rectangle.
This can be done as shown below:
Area = length*width
We can find the width of the path as shown below:
Let the width of the path be x.
The length of the pool is 28 meters.
The width of the pool is 20 meters.
The area of the pool including the path is given as:
Area = 1584 square meters
Length*width = 1584 square meters
[tex](28+x)(20+x) = 1584\\560 + 20x + 28x + x^2 = 1584\\x^2 + 48x + 560 - 1584 = 0\\x^2 + 48x - 1024 = 0\\x^2 + 64x - 16x - 1024 = 0\\x(x + 64) - 16(x + 64) = 0\\(x - 16)(x + 64) = 0[/tex]
Therefore, x = 16, x = -64
The width of the pool cannot be a negative value. Therefore, the width of the path is x = 16.
Therefore, we have found that the width of the path is 16 meters.
Learn more about the area of a rectangle here: https://brainly.com/question/25292087
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