2 The side length of a square tile is 200 mm and the side length of a square
floor is .
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?

Question

2 The side length of a square tile is 200 mm and the side length of a square
floor is

.
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?

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

**Given:**
- Side length of one square tile = 200 mm
- Side length of the square floor = 2.4 m

**Note:** To express ratios effectively, it's best to convert both measurements to the same unit. We'll convert meters to millimeters since 1 m = 1000 mm.

$$
2.4\, \text{m} = 2.4 \times 1000 = 2400\, \text{mm}
$$

---

### **a. Express the side lengths as a ratio**

**Tile side length:** 200 mm  
**Floor side length:** 2400 mm

The ratio of the side lengths is:

$$
\text{Tile} : \text{Floor} = 200\, \text{mm} : 2400\, \text{mm}
$$

Simplify the ratio by dividing both terms by 200:

$$
200 : 2400 = \frac{200}{200} : \frac{2400}{200} = 1 : 12
$$

**Answer:** The ratio of the side lengths is $$1 : 12$$.

---

### **b. Express the area of the floor and the area of one tile as a ratio**

First, calculate the areas.

**Area of one tile:**

$$
\text{Area}_{\text{tile}} = (\text{Side length})^2 = 200^2 = 40,\!000\, \text{mm}^2
$$

**Area of the floor:**

$$
\text{Area}_{\text{floor}} = (\text{Side length})^2 = 2400^2 = 5,\!760,\!000\, \text{mm}^2
$$

Now, form the ratio of the floor area to the tile area:

$$
\text{Floor Area} : \text{Tile Area} = 5,\!760,\!000\, \text{mm}^2 : 40,\!000\, \text{mm}^2
$$

Simplify the ratio by dividing both terms by 40,000:

$$
\frac{5,\!760,\!000}{40,\!000} : \frac{40,\!000}{40,\!000} = 144 : 1
$$

**Answer:** The ratio of the floor area to one tile area is $$144 : 1$$.

---

### **c. How many tiles are required to cover the floor?**

From part **b**, we've established that:

$$
\text{Floor Area} : \text{Tile Area} = 144 : 1
$$

This means that 144 tiles are required to cover the entire floor.

**Answer:** **144 tiles** are needed to cover the floor.
**a. Side length ratio:** 1 : 12 **b. Area ratio:** 144 : 1 **c. Number of tiles needed:** 144

2 The side length of a square tile is 200 mm and the side length of a square
floor is .
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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Latest Geometry Questions

2 The side length of a square tile is 200 mm and the side length of a square floor is . 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?

Upstudy AI Solution

Answer

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Beyond the Answer

Related Questions

Latest Geometry Questions

2 The side length of a square tile is 200 mm and the side length of a square
floor is .
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?