Answer:
The height of the larger prism is;
[tex]41.7\text{ cm}[/tex]Explanation:
Given that the surface area of two similar prisms are 144cm^2 and 625cm^2;
[tex]\begin{gathered} A_1=144cm^2 \\ A_2=625cm^2 \end{gathered}[/tex]Given that the height of the smaller prism is 20cm;
[tex]h_1=20\operatorname{cm}[/tex]Since they are similar, the ratio between their area and heights can be expressed as;
[tex]\frac{h_2}{h_1}=\sqrt[]{\frac{A_2}{A_1}}[/tex][tex]h_2=h_1\sqrt[]{\frac{A_2}{A_1}}[/tex]substituting the given values;
[tex]\begin{gathered} h_2=h_1\sqrt[]{\frac{A_2}{A_1}} \\ h_2=20_{}\sqrt[]{\frac{625}{144_{}}} \\ h_2=41.66667 \\ h_2=41.7 \end{gathered}[/tex]Therefore, the height of the larger prism is;
[tex]41.7\text{ cm}[/tex]