Since the photo and the poster are similar, their corresponding dimensions are proportional. The proportion between the length and width of both the photo and the poster can be used to solve for the unknown width of the poster.

We know the following:

• Length of the photo = 3 inches
• Width of the photo = 5 inches
• Length of the poster = 21 inches

Let $w$ represent the width of the poster.

Set up the proportion between the lengths and widths of the photo and the poster:

$\frac{\text{Length of the photo}}{\text{Length of the poster}} = \frac{\text{Width of the photo}}{\text{Width of the poster}}$

Substitute the known values:

$\frac{3}{21} = \frac{5}{w}$

Now, solve for $w$:

$w = \frac{5 \times 21}{3} = 35 \, \text{inches}$

Thus, the width of the poster is 35 inches.

Would you like a further breakdown or have any questions?

Here are 5 related questions:

1. How would the width change if the length of the poster were 30 inches instead?
2. What is the area of the original photo and the enlarged poster?
3. How does the ratio of areas compare to the ratio of the lengths?
4. If another photo with different dimensions is enlarged to the same length, how would you calculate the new width?
5. How does the concept of similarity apply to other geometric shapes?

Tip: When two shapes are similar, their corresponding sides are proportional, which means their dimensions scale by the same ratio.