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.

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 (\(2 \times 2 = 4\)).