We can express the area of a triangle as half the product of its base and height:
[tex]A=\frac{b\cdot h}{2}[/tex]Then, we can express the base in function of the known variables (area and height) as:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ 2A=b\cdot h \\ b=\frac{2A}{h} \end{gathered}[/tex]We replace with the known values (A=432 sq in, h=48 in) and calculate the base b:
[tex]b=\frac{2\cdot432\text{ in}^2}{48\text{ in}}=18\text{ in}[/tex]Answer: the base is 18 inches.
