Answer:
40 un.
Step-by-step explanation:
The diagonals of the rhombus bisect each other at right angle. This gives us that
- [tex]VS=\dfrac{1}{2}VN=6\ un.;[/tex]
- [tex]ES=\dfrac{1}{2}EU=8\ un. ;[/tex]
- [tex]\angle VSE=90^{\circ}.[/tex]
By the Pythagorean theorem,
[tex]VE^2=VS^2+ES^2,\\ \\VE^2=6^2+8^2,\\ \\ VE^2=36+64,\\ \\VE^2=100,\\ \\VE=10\ un.[/tex]
The sides of the rhombus are all of the same length, then the perimeter of the rhombus is
[tex]P_{VENU}=4\cdot 10=40\ un.[/tex]
