The dimensions of John’s painting are 16 cm by 12 cm. Using a photocopier, John prints a smaller copy that has the same dimension ratio as the original. Which is the size of John’s copy?

Select an Answer
A
Height =10 cm

Width = 6 cm

B
Height = 4 cm

Width = 3 cm

C
Height = 6 cm

Width = 8 cm

D
Height = 8 cm

Width = 12 cm

To solve this, we need to ensure that the smaller copy of the painting retains the same ratio as the original dimensions of 16 cm by 12 cm.

The ratio of the original painting is:

\[
\text{Ratio} = \frac{16}{12} = \frac{4}{3}
\]

For the smaller copy, the dimensions must maintain this same 4:3 ratio. Let's check each option to see which one satisfies this ratio:

- **Option A**: Height = 10 cm, Width = 6 cm  
\[
\frac{10}{6} = \frac{5}{3} \quad \text{(This is not } 4:3\text{)}
\]

- **Option B**: Height = 4 cm, Width = 3 cm  
\[
\frac{4}{3} = \frac{4}{3} \quad \text{(This matches the ratio)}
\]

- **Option C**: Height = 6 cm, Width = 8 cm  
\[
\frac{6}{8} = \frac{3}{4} \quad \text{(This is not } 4:3\text{)}
\]

- **Option D**: Height = 8 cm, Width = 12 cm  
\[
\frac{8}{12} = \frac{2}{3} \quad \text{(This is not } 4:3\text{)}
\]

The only option that maintains the original ratio of 4:3 is **Option B: Height = 4 cm, Width = 3 cm**.

Thus, the correct answer is **B**.

Would you like more details or have any questions?  
Here are 5 related questions for further understanding:

1. How do you calculate the ratio of two dimensions?
2. How can you scale a shape while keeping the same ratio?
3. What happens if the ratio changes when scaling an object?
4. Can a non-rectangular shape maintain a dimension ratio when scaled?
5. How do you reverse the scaling process to find the original dimensions?

**Tip:** To check if two shapes are proportional, always reduce the ratios to their simplest form.

The dimensions of John’s painting are 16 cm by 12 cm. Using a photocopier, John prints a smaller copy that has the same dimension ratio as the original. Which is the size of John’s copy?

A. Height = 10 cm, Width = 6 cm

B. Height = 4 cm, Width = 3 cm

C. Height = 6 cm, Width = 8 cm

D. Height = 8 cm, Width = 12 cm

Learn how to solve a ratio problem involving the dimensions of a painting and its scaled-down copy. This problem tests your understanding of ratios and proportions, with a solution that ensures the correct scaling is applied. Suitable for students in Grades 6-8.

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