Answer
a. 14 ft²
b. length = 7 ft, width = 2 ft
c.
Step-by-step explanation
a. The dresser has a shape of a rectangular prism. Then, the volume of the dresser is calculated as follows:
[tex]V=\text{ Area of the base}\cdot\text{ height}[/tex]Substituting with V = 42 cubic ft, and height = 3 ft, and solving for the area of the base:
[tex]\begin{gathered} 42=\text{ Area of the base }\cdot3 \\ \frac{42}{3}=\text{ Area of the base} \\ 14\text{ ft}^2\text{ = Area of the base} \end{gathered}[/tex]b. The base of the dresser is a rectangle. Then, the area of the base is calculated as follows:
[tex]A=\text{ length}\cdot\text{ width}[/tex]Assuming the length is 7 ft, and substituting A = 14 sq ft, the width must be:
[tex]\begin{gathered} 14=7\cdot\text{ width} \\ \frac{14}{7}=\text{ width} \\ 2\text{ ft = width} \end{gathered}[/tex]