Answer:
408 tiles
Step-by-step explanation:
To find the number of tiles needed, we can first calculate the total area of the wall to be tiled and then divide it by the area of each tile.
The area of a rectangle is given by the formula:
[tex] \textsf{Area} = \textsf{length} \times \textsf{width} [/tex]
Given that the wall is 42 inches long and 29 3/4 inches high:
[tex] \textsf{Area of the wall} = 42 \times \left(29 + \dfrac{3}{4}\right) [/tex]
To simplify the calculation, let's convert the mixed number to an improper fraction:
[tex] \textsf{Area of the wall} = 42 \times \left(\dfrac{116}{4} + \dfrac{3}{4}\right) [/tex]
Now, add the fractions:
[tex] \textsf{Area of the wall} = 42 \times \dfrac{119}{4} [/tex]
[tex] \textsf{Area of the wall} = \dfrac{42 \times 119}{4} [/tex]
Now, calculate the area:
[tex] \textsf{Area of the wall} = \dfrac{4998}{4} [/tex]
[tex] \textsf{Area of the wall} = 1249.5 \, \textsf{square inches} [/tex]
Now, find the area of one tile:
[tex] \textsf{Area of one tile} = \left(\dfrac{7}{4}\right)^2 [/tex]
[tex] \textsf{Area of one tile} = \dfrac{49}{16} [/tex]
Now, find the number of tiles needed:
[tex] \textsf{Number of tiles} = \dfrac{\textsf{Area of the wall}}{\textsf{Area of one tile}} [/tex]
[tex] \textsf{Number of tiles} = \dfrac{1249.5}{\dfrac{49}{16}} [/tex]
[tex] \textsf{Number of tiles} = \dfrac{1249.5 \times 16}{49} [/tex]
Now, calculate:
[tex] \textsf{Number of tiles} = \dfrac{19992}{49} [/tex]
[tex] \textsf{Number of tiles} \approx 408 [/tex]
Therefore, Ms. Zavala will need approximately 408 tiles to tile the rectangular wall.
Answer:
408 tiles
Step-by-step explanation:
To find the number of tiles Ms. Zavala needs to tile the rectangular wall behind the kitchen sink, we need to divide the length and the height of the area by the side length of the square tile.
The length of the area to be tiled is 42 inches. Therefore, the number of tiles needed along one row can be found by dividing 42 inches by the side length of one square tile (1³/₄ inches):
[tex]\begin{aligned}\textsf{Number of tiles (length)}&=42 \div 1\frac{3}{4}\\\\&=42 \div \dfrac{4\times 1+3}{4}\\\\&=42 \div \dfrac{7}{4}\\\\&=\dfrac{42}{1} \times \dfrac{4}{7}\\\\&=\dfrac{168}{7}\\\\&=24\end{aligned}[/tex]
The height of the area to be tiled is 29³/₄ inches. Therefore, the number of tiles needed along one column can be found by dividing 29³/₄ inches by the side length of one square tile (1³/₄ inches):
[tex]\begin{aligned}\textsf{Number of tiles (height)}&=29\frac{3}{4}\div 1\frac{3}{4}\\\\&=\dfrac{29\times 4+3}{4}\div \dfrac{1\times 4+3}{4}\\\\&=\dfrac{119}{4}\div \dfrac{7}{4}\\\\&=\dfrac{119}{4}\times\dfrac{4}{7}\\\\&=\dfrac{476}{28}\\\\&=17\end{aligned}[/tex]
To find the total number of tiles, we multiply the number of tiles needed to complete one row by the total number of tiles needed to complete one column:
[tex]\begin{aligned}\textsf{Total number of tiles}&=24\times 17\\\\&=408\end{aligned}[/tex]
Therefore, Ms. Zavala needs exactly 408 tiles to tile the rectangular area behind the kitchen sink.
