Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.