A total of 364 paper straws of equal length were used to construct two types of

Choice A is correct. It's given that $364$ paper straws of equal length were used to construct triangles and rectangles, where no two polygons had a common side. It's also given that the equation $3x+4y=364$ represents this situation, where $x$ is the number of triangles constructed and $y$ is the number of rectangles constructed. The equation $\left(x,y\right)=\left(24,73\right)$ means that if $x=24$, then $y=73$. Substituting $24$ for $x$ and $73$ for $y$ in $3x+4y=364$ yields $3\left(24\right)+4\left(73\right)=364$, or $364=364$, which is true. Therefore, in this context, the equation $\left(x,y\right)=\left(24,73\right)$ means that if $24$ triangles were constructed, then $73$ rectangles were constructed. 

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.