In a right triangle, the area is given by half of the product between the height and the base.
[tex]A=\frac{b\times h}{2}[/tex]
We already know the height and the area, if we plug those values on this formula we can solve it for the base
[tex]\frac{25}{12}=\frac{b\times\frac{5}{3}}{2}[/tex]
Solving for b, we have
[tex]\begin{gathered} \frac{25}{12}=\frac{b\times\frac{5}{3}}{2} \\ \frac{25}{12}\times2=\frac{b\times\frac{5}{3}}{2}\times2 \\ \frac{25}{6}=b\times\frac{5}{3} \\ b=\frac{\frac{25}{6}}{\frac{5}{3}} \\ b=\frac{25}{6}\times\frac{3}{5} \\ b=\frac{25\times3}{6\times5} \\ b=\frac{25}{5}\times\frac{3}{6} \\ b=5\times\frac{1}{2} \\ b=\frac{5}{2} \end{gathered}[/tex]
The base is equal to 5/2 cm.
