#### Answer

$\dfrac{15\sqrt{2}}{2} \text{ and } \dfrac{15\sqrt{2}}{2}$

#### Work Step by Step

The diagonal and the two sides of the square form a right triangle with the hypotenuse equal to $15.$
Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $
a=b
$ and $
c=15
,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
a^2+a^2=15^2
\\\\
2a^2=225
\\\\
a^2=\dfrac{225}{2}
\\\\
a=\sqrt{\dfrac{225}{2}}
\\\\
a=\sqrt{\dfrac{225}{2}\cdot\dfrac{2}{2}}
\\\\
a=\sqrt{\dfrac{225}{4}\cdot2}
\\\\
a=\sqrt{\left( \dfrac{15}{2}\right)^2\cdot2}
\\\\
a=\dfrac{15}{2}\sqrt{2}
\\\\
a=\dfrac{15\sqrt{2}}{2}
.\end{array}
Hence, the missing sides measure $
\dfrac{15\sqrt{2}}{2} \text{ and } \dfrac{15\sqrt{2}}{2}
$ units.