Lana has an illustration she wants enlarged
It is 6 cm wide and has an area of .
She wants both the width and the height
doubled.

Ask by Cox Reese. in Australia

Jan 05,2025

Question

Lana has an illustration she wants enlarged It is 6 cm wide and has an area of $$ 48 \mathrm{~cm}^{2} $$. She wants both the width and the height doubled.

UpStudy AI · Accepted Answer

Certainly! Let's walk through the steps to determine the new dimensions and area of Lana's enlarged illustration.

### **Given:**
- **Original Width (W₁):** 6 cm
- **Original Area (A₁):** 48 cm²

### **Step 1: Determine the Original Height**

The area of a rectangle is calculated by multiplying its width by its height. Therefore, we can find the original height (H₁) using the formula:

$$
\text{Area} = \text{Width} \times \text{Height}
$$

$$
48\, \text{cm}² = 6\, \text{cm} \times H₁
$$

Solving for $$ H₁ $$:

$$
H₁ = \frac{48\, \text{cm}²}{6\, \text{cm}} = 8\, \text{cm}
$$

**Original Dimensions:**
- **Width:** 6 cm
- **Height:** 8 cm

### **Step 2: Double the Width and Height**

Lana wants to double both the width and the height.

$$
\text{New Width (W₂)} = 2 \times W₁ = 2 \times 6\, \text{cm} = 12\, \text{cm}
$$

$$
\text{New Height (H₂)} = 2 \times H₁ = 2 \times 8\, \text{cm} = 16\, \text{cm}
$$

**Enlarged Dimensions:**
- **Width:** 12 cm
- **Height:** 16 cm

### **Step 3: Calculate the New Area**

Using the enlarged dimensions:

$$
\text{New Area (A₂)} = W₂ \times H₂ = 12\, \text{cm} \times 16\, \text{cm} = 192\, \text{cm}²
$$

### **Summary:**
- **Original Dimensions:** 6 cm (width) × 8 cm (height) = 48 cm²
- **Enlarged Dimensions:** 12 cm (width) × 16 cm (height) = 192 cm²

**So, when Lana doubles both the width and the height of her illustration, the new area becomes 192 cm².** This is four times the original area since both dimensions are doubled ($$2 \times 2 = 4$$).
Lana's enlarged illustration will be 12 cm wide and 16 cm tall, with an area of 192 cm².

Lana has an illustration she wants enlarged
It is 6 cm wide and has an area of .
She wants both the width and the height
doubled.

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Lana has an illustration she wants enlarged It is 6 cm wide and has an area of . She wants both the width and the height doubled.