To find the width of the suitcase, we can use the formula for the volume of a rectangular prism, which is:
\[ V = B \times h \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.
- Calculate the area of the base \( B \). The base is a rectangle with a length \( l \) and width \( w \):
\[ B = l \times w \]
Given:
- Length \( l = 10 \) inches
- Height \( h = 20 \) inches
- Volume \( V = 2,600 \) cubic inches
Since we know the height of the suitcase, we can rearrange the volume formula to solve for \( B \):
\[ B = \frac{V}{h} = \frac{2600}{20} = 130 \text{ square inches} \]
- Now, plug in the length to find the width:
\[ B = l \times w \]
Substituting in the values we have:
\[ 130 = 10 \times w \]
- Now solve for \( w \):
\[ w = \frac{130}{10} = 13 \text{ inches} \]
Thus, the width of the suitcase is 13 inches.