Respuesta :
Answer:
b. Regardless of the size she chooses, the area of the wall that is being tiled is the same
Reason: The area of the wall must be the same as the area of the tiles irrespective of the measure of tiles.
c. She will need four 4-inch tiles to cover the same area as one 8-inch tile.
Reason: Area of one 8-inches = 4 *area of one 4-inch tiles
64 = 4*16
64 = 64
Step-by-step explanation:
Let's find the area of the rectangular wall of the bathroom.
Area of the rectangular wall = length x width
= 80 x 40
= 320 square inches.
Now let's find the area of each tiles.
All the tiles are in square shapes.
Area of the tile which is 8 inches in length = 8 x 8 = 64 square inches
Area of the tile which is 4 inches in length = 4 x 4 = 16 square inches
Area of the tile which is 2 inches in length = 2 x 2 = 4 square inches
Let's find the number of tiles needed to tile the rectangular wall.
The number 8 inches tiles needed = [tex]\frac{320}{64} = 5[/tex] tiles
The number 4 inches tiles needed = [tex]\frac{320}{16} = 20[/tex] tiles
The number 2 inches tiles needed = [tex]\frac{320}{4} = 80[/tex] tiles
Now let's find the correct statements.
b. Regardless of the size she chooses, the area of the wall that is being tiled is the same
Reason: The area of the wall must be the same as the area of the tiles irrespective of the measure of tiles.
c. She will need four 4-inch tiles to cover the same area as one 8-inch tile.
Reason: Area of one 8-inches = 4 *area of one 4-inch tiles
64 = 4*16
64 = 64
The area of a shape is simply the amount of space occupied by the shape. The true statements are:
- Regardless of the size she chooses, the area of the wall that is being tiled is the same
- She will need four 4-inch tiles to cover the same area as one 8-inch tile.
Given that:
Lengths of available tiles: 8 inches, 4 inches and 2 inches
(a) The number of tiles will be the same, regardless the size.
This is incorrect, because the bigger the tiles, the smaller the number of tiles to use.
(b) The area of the wall is the same, regardless the size
This is the true because the area of the wall is independent of the size of tiles chosen.
The area of the tiles will always be 3200 inches square:
[tex]Area = 80in \times 40in[/tex]
[tex]Area = 3200in^2[/tex]
(c) Two 2-inch tiles will cover the same area as one 4-inch
The area of the 2-inch tiles is:
[tex]A_1 = 2in \times 2in[/tex]
[tex]A_1 = 4in^2[/tex]
The area of the 4-inch tiles is:
[tex]A_2 = 4in \times 4in[/tex]
[tex]A_2 = 16in^2[/tex]
Divide both areas
[tex]\frac{A_2}{A_1} = \frac{16in^2}{4in^2} = 4[/tex]
This means that she needs four 2-inch tiles to cover the same area as one 4-inch tiles.
(c) is incorrect
(d) Four 4-inch tiles will cover the same area as one 8-inch
The area of the four 4-inch tiles is:
[tex]A_1 =4 \times 4in \times 4in[/tex]
[tex]A_1 = 64in^2[/tex]
The area of the 8-inch tiles is:
[tex]A_2 = 8in \times 8in[/tex]
[tex]A_2 = 64in^2[/tex]
Divide both areas
[tex]\frac{A_2}{A_1} = \frac{64in^2}{64in^2} = 1[/tex]
This means that she needs four 4-inch tiles to cover the same area as one 8-inch tiles.
(d) is correct
(e) Quarter 8-inch tiles will cover the same area as one 2-inch
The area of the one 2-inch tiles is:
[tex]A_1 = 4in^2[/tex]
The area of the quarter 8-inch tiles is:
[tex]A_2 = \frac14 \times 8in \times 8in[/tex]
[tex]A_2 = 16in^2[/tex]
Divide both areas
[tex]\frac{A_2}{A_1} = \frac{16in^2}{4in^2} = 4[/tex]
This means that she needs four 2-inch tiles to cover the same area as a quarter 8-inch tile.
(e) is incorrect
Hence, the true statements are:
- Regardless of the size she chooses, the area of the wall that is being tiled is the same
- She will need four 4-inch tiles to cover the same area as one 8-inch tile.
Read more about areas at:
https://brainly.com/question/16151549
