7. The distances from the space diagonal of a rectangular prism to the three edges that do not intersect it are $2 \sqrt{5}, \frac{30}{\sqrt{13}}, \frac{15}{\sqrt{10}}$, then the volume of the rectangular prism is $\qquad$
7.750

Analysis: Suppose the length, width, and height of the rectangular prism are $a, b, c$, respectively, then the distances from the diagonal to the edges are
$$
\frac{a b}{\sqrt{a^{2}+b^{2}}}, \frac{b c}{\sqrt{b^{2}+c^{2}}}, \frac{a c}{\sqrt{a^{2}+c^{2}}} \text {, hence }\left\{\frac{a b}{\sqrt{a^{2}+b^{2}}}, \frac{b c}{\sqrt{b^{2}+c^{2}}}, \frac{a c}{\sqrt{a^{2}+c^{2}}}\right\}=\left\{2 \sqrt{5}, \frac{30}{\sqrt{13}}, \frac{15}{\sqrt{10}}\right\} \text {; }
$$

Solving yields: $\{a, b, c\}=\{5,10,15\}$, thus the volume is 750.