The question in the image asks:

A small painting has a height of 15 cm and is scaled up to a height of 45 cm. What is the scale factor?

To find the scale factor, we can use the following formula:

$\text{Scale factor} = \frac{\text{New height}}{\text{Original height}}$

Given:

• Original height = 15 cm
• New height = 45 cm

Now, applying the formula:

$\text{Scale factor} = \frac{45}{15} = 3$

Thus, the scale factor is 3.

Would you like more details or have any other questions?

Here are 5 related questions to further explore:

1. If the painting's width was originally 10 cm, what is its new width after the scaling?
2. How would you calculate the scale factor if the painting was scaled down instead of up?
3. If another painting has a scale factor of 2 and its original height is 20 cm, what is the new height?
4. Can a scale factor be a fraction? What does that imply about the size of the scaled object?
5. What would the new area of the painting be if both dimensions (height and width) are scaled by the same factor?

Tip: When scaling an object, the area increases by the square of the scale factor, so a scale factor of 3 means the area is multiplied by 9 (since $3^2 = 9$).