Question

a. The length of one side of a square tile is \(1 \frac{1}{2}\) feet. Determine the area of the tile in square feet \(\left(\text { use } A=s^{2}\right)\) b. How many tiles would you need to cover a 9 -foot by 10 -foot bathroom floor, assuming no errors or waste?

Short answer

Answer: 40 tiles

Step-by-step solution

Find the area of the square tile.

Since we know that the length of one side of the square tile is \(1\frac{1}{2}\) feet, we can convert this mixed number to an improper fraction. To do this, we multiply the whole part (1) by the denominator (2) and add the numerator (1): \((1 \times 2) + 1 = 3\). So, the improper fraction is \(\frac{3}{2}\) feet. Now, use the formula \(A = s^2\). Plug in the value of \(s\): \(A=\left(\frac{3}{2}\right)^{2}=\frac{9}{4}\) The area of the tile is \(\frac{9}{4}\) square feet.

Calculate the number of tiles needed to cover the bathroom floor.

To find the total tiles needed to cover the bathroom floor, we first need to find the area of the floor. The bathroom floor measures 9 feet by 10 feet. Multiply these values to get the area of the floor: \(A_{\text{floor}} = 9 \times 10 = 90\) square feet. Now, we can divide the area of the floor by the area of one tile to find out how many tiles are needed to cover the floor: \(\text{Number of tiles} = \frac{A_{\text{floor}}}{A_{\text{tile}}} = \frac{90}{\frac{9}{4}} = \frac{90}{1} \times \frac{4}{9} = 10\times 4 = 40\) So, we would need 40 tiles to cover the bathroom floor without waste or errors.