Question

Jenna is creating a mural for her bedroom wall. She would like to copy a picture that is 2 inches by 2.5 inches. She uses a copy machine to enlarge it by a scale factor of 4. Then she projects it on her wall by a scale factor of 12.



Part A

What are the dimensions of the mural? Write the smaller dimension first and the larger dimension second.

inches by
inches



Part B

Are both of the enlarged pictures similar to the original? Write yes or no.

Answer 1

To answer the questions, we will first calculate the dimensions of the mural by considering the enlargements made by Jenna.

**Part A: Dimensions of the Mural**

1. **Original dimensions of the picture**: 2 inches by 2.5 inches.
2. **First Enlargement (Scale factor 4)**:
- Smaller dimension: \(2 \text{ inches} \times 4 = 8 \text{ inches}\)
- Larger dimension: \(2.5 \text{ inches} \times 4 = 10 \text{ inches}\)

After the first enlargement, the dimensions are 8 inches by 10 inches.

3. **Second Enlargement (Scale factor 12)**:
- Smaller dimension: \(8 \text{ inches} \times 12 = 96 \text{ inches}\)
- Larger dimension: \(10 \text{ inches} \times 12 = 120 \text{ inches}\)

So, the dimensions of the mural after both enlargements are **96 inches by 120 inches**.

**Answer for Part A**: 96 inches by 120 inches.

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**Part B: Similarity of Enlarged Pictures**

To determine if both enlarged pictures are similar to the original, we need to check if the aspect ratios of the enlarged pictures are the same as that of the original picture.

1. **Original picture aspect ratio**:
- Ratio = \(\frac{2.5}{2} = 1.25\)

2. **First Enlarged picture (8 inches by 10 inches) aspect ratio**:
- Ratio = \(\frac{10}{8} = 1.25\)

3. **Second Enlarged picture (96 inches by 120 inches) aspect ratio**:
- Ratio = \(\frac{120}{96} = 1.25\)

Since both enlarged pictures have the same aspect ratio as the original picture, they are similar to the original.

**Answer for Part B**: Yes.