floor is $$ 2,4 \mathrm{~m} $$. a Express the side lengths as a ratio. b Express the area of the floor and the area of one tile as a ratio. c How many tiles are required to cover the floor?

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Certainly! Let's address each part of your problem step by step.

**Given:**
- The floor dimensions are $$ 2 \, \text{m} $$ by $$ 4 \, \text{m} $$.
- We'll assume that the tiles are square-shaped with each side measuring $$ 0.5 \, \text{m} $$ (since the tile size wasn't specified). If your tile size is different, you can adjust the calculations accordingly.

---

### **a. Express the Side Lengths as a Ratio**

**Floor Dimensions:**
- Length = $$ 2 \, \text{m} $$
- Width = $$ 4 \, \text{m} $$

**Ratio of Length to Width:**
$$
\text{Ratio} = \frac{\text{Length}}{\text{Width}} = \frac{2}{4} = \frac{1}{2}
$$
**Simplified Ratio:** $$ 1 : 2 $$

---

### **b. Express the Area of the Floor and the Area of One Tile as a Ratio**

**Area Calculations:**

1. **Floor Area ($$ A_{\text{floor}} $$):**
$$
A_{\text{floor}} = \text{Length} \times \text{Width} = 2 \, \text{m} \times 4 \, \text{m} = 8 \, \text{m}^2
$$

2. **Tile Area ($$ A_{\text{tile}} $$):**
$$
A_{\text{tile}} = \text{Side} \times \text{Side} = 0.5 \, \text{m} \times 0.5 \, \text{m} = 0.25 \, \text{m}^2
$$

**Ratio of Floor Area to Tile Area:**
$$
\text{Ratio} = \frac{A_{\text{floor}}}{A_{\text{tile}}} = \frac{8}{0.25} = 32
$$
**Expressed as a Ratio:** $$ 32 : 1 $$

---

### **c. How Many Tiles Are Required to Cover the Floor?**

**Number of Tiles Needed ($$ N $$):**
$$
N = \frac{A_{\text{floor}}}{A_{\text{tile}}} = \frac{8 \, \text{m}^2}{0.25 \, \text{m}^2} = 32
$$

**Therefore, you will need **32 tiles** to cover the floor completely.**

---

**Summary:**
- **a.** The side lengths of the floor are in the ratio **1 : 2**.
- **b.** The area of the floor to the area of one tile is in the ratio **32 : 1**.
- **c.** **32 tiles** are required to cover the entire floor.

*If your tile size differs from $$ 0.5 \, \text{m} \times 0.5 \, \text{m} $$, simply replace the tile area in part b and recalculate accordingly.*
**a.** The floor's length and width are in the ratio **1:2**. **b.** The area of the floor to one tile is in the ratio **32:1**. **c.** **32 tiles** are needed to cover the floor.

floor is \( 2,4 \mathrm{~m} \). a Express the side lengths as a ratio. b Express the area of the floor and the area of one tile as a ratio. c How many tiles are required to cover the floor?

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