Question

□ complete the following problems.performance task: house flippers part 1you are a house flipper who has just purchased a house and you are eager to fix it up so that you can put it back on the market. for one project, you plan to put wallpaper in both the family room and the living room. you will not put wallpaper across any of the doorways.for this performance task, use these definitions to make sense of the problem and to calculate your final answers.- house flipper - a real estate investor who buys a house that needs repair and performs necessary renovations and repairs before reselling it at a higher price for a profit (\fix and flip\).- living room - room of the home reserved for guests, special occasions, and the display of items such as antiques or artwork.- family room - less formal room of the home (compared to the living room) in both function and furnishings and is located away from the main entrance.family room1. write an expression (or equation) that represents the number of square feet of wallpaper you will need if the height of the family room is x feet, with a length and width that are each 3 times the height of the room. the family room has 1 door, which is 3 feet wide and 7 feet tall. (2 points)note: find and add the expressions for the area of each of the walls. remember that one of the four walls has a door.living room2. write the expression (or equation) for the amount of wallpaper in square feet you need to cover the living room, which is the same height and width as the family room, but it has a length that is 5 times greater than the height. the living room has 2 doors. (2 points)note: remember that there are two doors.

Explanation:

Step1: Calculate total wall area of family room

The family room is a rectangular prism with 4 walls: 2 walls of dimensions $3x \times x$ and 2 walls of dimensions $3x \times x$.
Total wall area = $2(3x \times x) + 2(3x \times x) = 2(3x^2) + 2(3x^2) = 6x^2 + 6x^2 = 12x^2$

Step2: Subtract door area for family room

Door area = $3 \times 7 = 21$ square feet.
Expression for family room wallpaper: $12x^2 - 21$

Step3: Calculate total wall area of living room

The living room has 2 walls of dimensions $3x \times x$ and 2 walls of dimensions $5x \times x$.
Total wall area = $2(3x \times x) + 2(5x \times x) = 2(3x^2) + 2(5x^2) = 6x^2 + 10x^2 = 16x^2$

Step4: Subtract 2 door areas for living room

Total door area = $2 \times (3 \times 7) = 2 \times 21 = 42$ square feet.
Expression for living room wallpaper: $16x^2 - 42$

Answer:

1. $12x^2 - 21$
2. $16x^2 - 42$