Question 1200305: Let’s say you are remodeling your room. You want to determine various measurements using
polynomial expressions. Your room is
8x
feet by
3x
feet.
1. How much border should you purchase is you are putting border around the edge of the top of
your walls? (Assume there is wall space above the opening for the door).
2. On the floor, you will need to purchase wood floor panels. How much should you buy to
cover the entire floor of your bedroom?
3. Your mom just told you that she will give you your sister’s bedroom which as 3 more feet of
length and 2 less feet of width. What is the new amount of border you will need to purchase?
4. In the new room, what is the new amount of flooring you will need to purchase?
5. What is the difference in the size of the new bedroom and the original bedroom?
Answer by GingerAle(43)   (Show Source):
You can put this solution on YOUR website! Certainly, let's figure out the measurements for your room remodel!
**1. Border for the top of the walls:**
* **Find the perimeter:**
* Perimeter = 2 * (Length + Width)
* Perimeter = 2 * (8x + 3x) = 2 * 11x = 22x feet
* **You should purchase 22x feet of border.**
**2. Flooring for the original room:**
* **Find the area:**
* Area = Length * Width
* Area = 8x * 3x = 24x² square feet
* **You should purchase 24x² square feet of flooring.**
**3. Border for the new room:**
* **New room dimensions:**
* Length = 8x + 3 = (8x + 3) feet
* Width = 3x - 2 = (3x - 2) feet
* **Find the new perimeter:**
* Perimeter = 2 * (Length + Width)
* Perimeter = 2 * [(8x + 3) + (3x - 2)] = 2 * (11x + 1) = 22x + 2 feet
* **You should purchase 22x + 2 feet of border for the new room.**
**4. Flooring for the new room:**
* **Find the new area:**
* Area = Length * Width
* Area = (8x + 3) * (3x - 2)
* Area = 24x² - 16x + 9x - 6
* Area = 24x² - 7x - 6 square feet
* **You should purchase 24x² - 7x - 6 square feet of flooring for the new room.**
**5. Difference in size between the new and original bedrooms:**
* **Find the difference in area:**
* Difference = New Room Area - Original Room Area
* Difference = (24x² - 7x - 6) - 24x²
* Difference = -7x - 6 square feet
* **The new bedroom is 7x + 6 square feet smaller than the original bedroom.**
I hope this helps! Let me know if you have any other questions.
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