Question

Tara plans to put wallpaper on the walls of her room. She will not put the wallpaper across the doorway, which is 3 feet wide and 7 feet tall.

Find the expression which represents the number of square feet of wallpaper she will need if the height of her room is x feet, with a length and width that are each 3 times the height of the room. Assume that the walls are four rectangles.

Tara will need ___ square feet of wallpaper for her bedroom.

Answer 1

To find the expression representing the number of square feet of wallpaper Tara needs, calculate the area of the walls in her room. The expression is 12x^2 square feet.

Step-by-step explanation:

To find the expression which represents the number of square feet of wallpaper Tara will need, we need to calculate the area of the walls in her room. The length and width of the room are each 3 times the height of the room, so the length would be 3x and the width would be 3x as well.

The height of the room is x feet, so the area of each wall would be 3x * x = 3x^2 square feet. Since there are four walls, the total square feet of wallpaper needed would be 4 * 3x^2 square feet, which simplifies to 12x^2 square feet.

Therefore, Tara will need 12x^2 square feet of wallpaper for her bedroom.

Answer 2

First,

To calculate the total Area we need to add the area of every wall (4 of them) and subtract the area of the doorway.


Height of the room ...........x feet
Width ............ 3x feet
Length ............3x feet

As the width and length are the same, this means that

Area wall 1 = Area wall 2 = Area wall 3 = Area wall 4 = 3x*x = 3x²

A total = 3x² + 3x² + 3x²+ 3x² - (7 feet*3 feet)

A total = 12x² - 21 feet²