1. **State the problem:** We have two similar shapes, A and B. We need to: a) Calculate the scale factor from shape A to shape B. b) Find the value of $w$ on shape B. 2. **Recall the properties of similar shapes:** - Corresponding sides of similar shapes are proportional. - The scale factor is the ratio of any pair of corresponding sides. 3. **Calculate the scale factor:** Given: - Width of A = 4 cm - Width of B = 3 cm - Height of A = 12 cm - Height of B = 9 cm Calculate scale factor from A to B using widths: $$\text{scale factor} = \frac{\text{width of B}}{\text{width of A}} = \frac{3}{4}$$ Calculate scale factor from A to B using heights: $$\text{scale factor} = \frac{\text{height of B}}{\text{height of A}} = \frac{9}{12} = \frac{3}{4}$$ Both ratios agree, so the scale factor from A to B is $\frac{3}{4}$. 4. **Find the value of $w$:** Since shapes are similar, corresponding sides scale by the scale factor. Assuming $w$ corresponds to a side length in shape A, let that length be $w_A$. Then: $$w = w_A \times \frac{3}{4}$$ If $w_A$ is given or can be identified, substitute it here. Since the problem does not provide $w_A$, but asks for $w$ as a fraction, we assume $w_A$ is known or given in the image. If $w_A$ is the length of the corresponding side in shape A, then: $$w = w_A \times \frac{3}{4}$$ 5. **Summary:** a) Scale factor from shape A to shape B is $\frac{3}{4}$. b) Value of $w$ is $w = w_A \times \frac{3}{4}$, where $w_A$ is the corresponding length in shape A. Since the problem does not specify $w_A$, the answer is expressed in terms of $w_A$.