Answer:
The value of k is;
[tex]k=\frac{27}{8}[/tex]Explanation:
Given the two similar Pyramids with surface area;
[tex]\begin{gathered} A=29.16in^2 \\ B=2.56in^2 \end{gathered}[/tex]The scale factor is the ratio of their corresponding lengths. which will also be equal to the square root of the ratio of their corresponding Surface Area.
[tex]k=\frac{\text{Length dimension of Pyramid A}}{\text{Length dimension of Pyramid B}}=\sqrt[]{\frac{\text{Surface area of Pyramid A}}{\text{Surface area of Pyramid B}}}[/tex]Substituting the given surface areas;
[tex]\begin{gathered} k=\sqrt[]{\frac{29.16}{2.56}} \\ k=\sqrt[]{\frac{729}{64}} \\ k=\frac{27}{8} \end{gathered}[/tex]Therefore, the value of k is;
[tex]k=\frac{27}{8}[/tex]