7he width and height of a rectangle are in a ratio of $$ 9: 2 $$. a. Draw the rectangle, and divide its width and length into parts according to its aspect ratio. b. If the rectangle's perimeter is 220 cm , find its width and its height.

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## **Problem Statement**

The width and height of a rectangle are in a ratio of $$ 9:2 $$.

**a.** Draw the rectangle, and divide its width and length into parts according to its aspect ratio.

**b.** If the rectangle's perimeter is 220 cm, find its width and its height.

---

## **Solution**

### **Part a: Drawing and Dividing the Rectangle According to the Aspect Ratio**

**Understanding the Aspect Ratio:**

- The aspect ratio of the rectangle is given as $$ 9:2 $$. This means that for every 9 units of width, there are 2 units of height.

**Steps to Draw and Divide the Rectangle:**

1. **Draw the Rectangle:**
   - Begin by drawing a rectangle. The orientation (landscape or portrait) can be chosen based on convenience, but typically, the longer side represents the width.

2. **Divide the Width into 9 Equal Parts:**
   - Since the width is in a ratio of 9, divide the entire length of the width into 9 equal segments. You can mark these divisions using a ruler or by eye, ensuring each part is of equal length.

3. **Divide the Height into 2 Equal Parts:**
   - Similarly, divide the height of the rectangle into 2 equal segments, reflecting the ratio.

4. **Visualization:**
   - If you imagine the rectangle as a grid, the width will have 9 columns and the height will have 2 rows. This grid helps in visualizing the proportion between the width and height.

**Illustrative Example:**

```
+-------------------------+
|                         |
|                         |
+-------------------------+
```

- **Width:** Divided into 9 segments.
- **Height:** Divided into 2 segments.

---

### **Part b: Finding the Width and Height from the Perimeter**

**Given:**
- **Perimeter (P):** 220 cm
- **Aspect Ratio:** Width : Height = 9 : 2

**Let’s Define Variables:**
- Let $$ W $$ be the width.
- Let $$ H $$ be the height.
- Let the common multiplier be $$ x $$. Therefore:
  - $$ W = 9x $$
  - $$ H = 2x $$

**Perimeter Formula:**
$$
P = 2(W + H)
$$
Substitute the given perimeter and the expressions for $$ W $$ and $$ H $$:
$$
220 = 2(9x + 2x)
$$

**Simplify and Solve for $$ x $$:**
$$
220 = 2(11x) \
220 = 22x \
x = \frac{220}{22} \
x = 10
$$

**Find Width and Height:**
$$
W = 9x = 9 \times 10 = 90 \text{ cm} \
H = 2x = 2 \times 10 = 20 \text{ cm}
$$

**Therefore:**
- **Width ($$ W $$) =** 90 cm
- **Height ($$ H $$) =** 20 cm

---

## **Conclusion**

By understanding the aspect ratio and applying the perimeter formula, we've determined that:

- **Width of the rectangle is 90 cm**
- **Height of the rectangle is 20 cm**

This approach can be used generally for rectangles where the aspect ratio is known, allowing for the determination of side lengths based on perimeter or area constraints.
The width of the rectangle is 90 cm and the height is 20 cm.

7he width and height of a rectangle are in a ratio of \( 9: 2 \). a. Draw the rectangle, and divide its width and length into parts according to its aspect ratio. b. If the rectangle's perimeter is 220 cm , find its width and its height.

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