Question

Find the perimeter of the triangle

Answer 1

first off, something noteworthy is that we have two angles of 60°, that means that the angle atop is also 60°, so we really have an equilateral triangle, with an altitude or height as shown above, so

`\textit{height of an equilateral triangle}\\\\ h=\cfrac{s√(3)}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4√(15) \end{cases}\implies 4√(15)=\cfrac{s√(3)}{2}\implies 8√(15)=s√(3) \\\\\\ \cfrac{8√(15)}{√(3)}=s\implies \cfrac{8√(2\cdot 3)}{√(3)}=s\implies \cfrac{8√(2)\cdot √(3)}{√(3)}=s\implies 8√(2)=s \\\\[-0.35em] ~\dotfill`

`\stackrel{ \textit{\LARGE perimeter} }{8√(2)~~ + ~~8√(2)~~ + ~~8√(2)}\implies 24√(2)`