Question

niles is building a sunroom on the back of his house. he measured the area of the sunroom to be 9 ft. by 8 ft. he is ordering tiles for the floor. each tile has an area of 400 cm². about how many tiles should niles order to completely cover the floor?
a 168 tiles
b 66,890 tiles
c 1,673 tiles
d 2,195 tiles
e 6 tiles

Explanation:

Step1: Calculate area of sunroom in square feet

The sunroom is a rectangle with length \( 9 \, \text{ft} \) and width \( 8 \, \text{ft} \). The area of a rectangle is \( \text{length} \times \text{width} \), so the area \( A_{\text{ft}} = 9 \times 8 = 72 \, \text{ft}^2 \).

Step2: Convert square feet to square centimeters

We know that \( 1 \, \text{ft} = 30.48 \, \text{cm} \), so \( 1 \, \text{ft}^2=(30.48)^2 \, \text{cm}^2 \approx 929.03 \, \text{cm}^2 \). Then the area of the sunroom in square centimeters is \( A_{\text{cm}} = 72\times929.03 \approx 66890.16 \, \text{cm}^2 \).

Step3: Calculate number of tiles

Each tile has an area of \( 400 \, \text{cm}^2 \). The number of tiles \( n=\frac{A_{\text{cm}}}{\text{Area of one tile}}=\frac{66890.16}{400}\approx 167.225 \). Wait, wait, no, wait. Wait, I made a mistake in step 2? Wait, no, wait \( 1 \, \text{ft} = 30.48 \, \text{cm} \), so \( 1 \, \text{ft}^2=(30.48)^2 = 929.0304 \, \text{cm}^2 \). Then \( 72 \, \text{ft}^2 = 72\times929.0304 = 66890.1888 \, \text{cm}^2 \). Then number of tiles is \( \frac{66890.1888}{400}\approx 167.225 \), but the options have 168, 66890, 1673, 2195, 6. Wait, maybe I messed up the conversion. Wait, no, wait \( 1 \, \text{ft} = 30.48 \, \text{cm} \), so \( 1 \, \text{ft} = 30.48 \, \text{cm} \), so \( 9 \, \text{ft}=9\times30.48 = 274.32 \, \text{cm} \), \( 8 \, \text{ft}=8\times30.48 = 243.84 \, \text{cm} \). Then area of sunroom in \( \text{cm}^2 \) is \( 274.32\times243.84 \approx 66890 \, \text{cm}^2 \). Then number of tiles is \( \frac{66890}{400}=167.225 \), which is approximately 168 (since we can't order a fraction of a tile, we round up). Wait, but option C is 1673, D is 2195, B is 66890. Wait, no, wait I think I made a mistake in the conversion factor. Wait, no, \( 1 \, \text{ft} = 30.48 \, \text{cm} \), so \( 1 \, \text{ft}^2 = (30.48)^2 = 929.0304 \, \text{cm}^2 \). So 72 sq ft is 72929.0304 = 66890.1888 sq cm. Then divide by 400: 66890.1888 / 400 = 167.225, which is approximately 168. So the answer should be A. Wait, but let's check again. Wait, maybe the problem is that I used the wrong conversion? Wait, no, 1 foot is 30.48 cm, so 1 square foot is (30.48)^2 cm². So 72929.03 is about 66890, divided by 400 is about 167, which is close to 168. So the correct option is A.

Answer:

A. 168 tiles