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Sagot :
The area of the garden is the amount of space on the garden.
- The area of the total garden is (x + 15)(x + 20)
- The width of the pathway is 1 meter
The expression of the area
The dimensions of the garden is given as:
15 meters by 20 meters
Let the width of the pedestrian pathway be x.
So, the area of the total garden is:
[tex]Area=(x + 15)(x + 20)[/tex]
The width of the pathway
In (a), we have:
[tex]Area=(x + 15)(x + 20)[/tex]
The total area is given as: 336.
So, we have:
[tex](x + 15)(x + 20) = 336[/tex]
Expand
[tex]x^2 + 35x + 300 = 336[/tex]
Collect like terms
[tex]x^2 + 35x + 300 - 336 = 0[/tex]
Evaluate
[tex]x^2 + 35x - 36 = 0[/tex]
Expand
[tex]x^2 + 36x -x - 36 = 0[/tex]
Factorize
[tex]x(x + 36) -1(x +36) = 0[/tex]
Factor out x + 36
[tex](x + 36)(x -1) = 0[/tex]
Solve for x
x = -36 or x =1
The width cannot be negative.
Hence, the width of the pathway is 1 meter
Read more about areas at:
https://brainly.com/question/24487155
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