Question

write an expression 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 time the height of the room. the family room has 1 door, which is 3 feet wide and 7 feet tall.

Answer 1

Given

• room height is x feet
• room length is 3x feet
• room width is 3x feet
• a door 3 ft wide by 7 ft tall

Find

• The net area of the wall, excluding the door

Solution

The area of the wall, including the door, is the room perimeter multiplied by the height of the room. The room perimeter is the sum of the lengths of the four walls.

... gross wall area = (3x +3x +3x +3x)·x = 12x²

The area of the door is the product of its height and width.

... door area = (7 t)×(3 ft) = 21 ft²

Then the net wall area, exclusive of the door is ...

... net wall area = gross wall area - door area

... net wall area = 12x² -21 . . . . square feet