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A contractor is constructing the house shown in the figure. The cross section
up to the roof is in the shape of a rectangle. The area of the rectangular floor
of the house is 1500 square feet. Express the perimeter of the rectangular
floor, P, as a function of the width of the rectangle, X.

Sagot :

MrRoyal

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]

Read more about areas and perimeters at:

https://brainly.com/question/11957651

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