Question

What is the length in feet of the base of the triangle?

Answer 1

$\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ A=\frac{2}{5}\\ h=\frac{6}{5} \end{cases}\implies \cfrac{2}{5}=\cfrac{1}{2}b\left( \cfrac{6}{5} \right)\implies \cfrac{2}{5}=\cfrac{6b}{10}\implies \cfrac{2}{5}=\cfrac{3b}{5} \\\\\\ 10=15b\implies \stackrel{\textit{dividing both sides by 15}}{\cfrac{10}{15}=\cfrac{15b}{15}}\implies \cfrac{10}{15}=b\implies \cfrac{2}{3}=b$