Answer:
The measure of the diagonal is [tex]3\sqrt{6}\ units[/tex]
Step-by-step explanation:
Let
c -----> the diagonal of a square in units
a ----> the length side of a square
Remember that a square can be divided into two congruent right triangles
see the attached figure to better understand the problem
Applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+a^{2}[/tex]
we have
[tex]a=3\sqrt{3}\ units[/tex]
substitute
[tex]c^{2}=(3\sqrt{3})^{2}+(3\sqrt{3})^{2}[/tex]
[tex]c^{2}=54[/tex]
[tex]c=\sqrt{54}\ units[/tex]
simplify
[tex]c=3\sqrt{6}\ units[/tex]
