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The perimeter of the rectangular floor is the sum of its dimensions
The perimeter function is [tex]\mathbf{P(x) = \frac{2x^2 + 3000}x}[/tex]
The area of the rectangular floor is given as: 1500
The area of a rectangle is calculated as:
[tex]\mathbf{Area = xy}[/tex]
Where: x and y represents the width and the length of the floor, respectively.
So, we have:
[tex]\mathbf{xy = 1500}[/tex]
Make y the subject
[tex]\mathbf{y = \frac{1500}x}[/tex]
The perimeter of the rectangular floor is:
[tex]\mathbf{P = 2(x + y)}[/tex]
Substitute [tex]\mathbf{y = \frac{1500}x}[/tex]
[tex]\mathbf{P = 2(x + \frac{1500}x)}[/tex]
Take LCM
[tex]\mathbf{P = 2(\frac{x^2 + 1500}x)}[/tex]
Open bracket
[tex]\mathbf{P = \frac{2x^2 + 3000}x}[/tex]
Express as a function
[tex]\mathbf{P(x) = \frac{2x^2 + 3000}x}[/tex]
Hence, the perimeter function is [tex]\mathbf{P(x) = \frac{2x^2 + 3000}x}[/tex]
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