We have the following equation for the lateral surface area of a triangular prism:
[tex]A=h(a+b+c)[/tex]where a,b and c are the measures of the sides of the triangular base.
In this case, we have the following:
[tex]\begin{gathered} A=744 \\ a=6 \\ b=8 \\ c=10 \end{gathered}[/tex]using the formula, we get:
[tex]744=h(6+8+10)[/tex]now, we can solve for h to find the height:
[tex]\begin{gathered} h(6+8+10)=744 \\ \Rightarrow24h=744 \\ \Rightarrow h=\frac{744}{24}=31 \\ h=31 \end{gathered}[/tex]therefore, the height of the solid is 31 cm
