Digital photography allows pictures to be printed in almost any size you want. Suppose you want the length and width of the 4 inch by 6 inch picture to be $$ 40 \% $$ larger so it will fit an antique frame. What is the new area of the picture?

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To determine the new area of the picture after increasing both the length and width by $$ 40\% $$, follow these steps:

1. **Calculate the New Dimensions:**
   - **Original Length:** 4 inches
   - **Original Width:** 6 inches
   - **Increase by $$ 40\% $$:**
     $$
     \text{New Length} = 4 \text{ inches} \times 1.40 = 5.6 \text{ inches}
     $$
     $$
     \text{New Width} = 6 \text{ inches} \times 1.40 = 8.4 \text{ inches}
     $$

2. **Calculate the New Area:**
   $$
   \text{New Area} = \text{New Length} \times \text{New Width} = 5.6 \text{ inches} \times 8.4 \text{ inches}
   $$
   $$
   \text{New Area} = 47.04 \text{ square inches}
   $$

**Alternatively,** you can use the scaling factor approach:
   - Since both dimensions are increased by $$ 40\% $$, the area increases by $$ 1.40^2 = 1.96 $$ times.
   - **Original Area:** $$ 4 \times 6 = 24 $$ square inches
   - **New Area:** $$ 24 \times 1.96 = 47.04 $$ square inches

**Final Answer:**  
After the increase, the picture has an area of **47.04 square inches**.
The new area of the picture is 47.04 square inches.

Digital photography allows pictures to be printed in almost any size you want. Suppose you want the length and width of the 4 inch by 6 inch picture to be \( 40 \% \) larger so it will fit an antique frame. What is the new area of the picture?

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