Answer: Perimeter of the rhombus is 20 units.
Step-by-step explanation:
Since we have given that
The vertices of rhombus DEFG whose vertices are as follows:
D(1, 4), E(4, 0), F(1, –4), and G(–2, 0)
As shown in the figure below:
Distance between DE is given by
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\D=\sqrt{(4-1)^2+(0-4)^2}\\\\D=\sqrt{3^2+4^2}\\\\D=\sqrt{9+16}\\\\D=\sqrt{25}\\\\D=5\ units[/tex]
Since it is a rhombus all sides will be equal to each other,
So, Perimeter of rhombus is given by
[tex]4\times Side\\\\=4\times 5\\\\=20\ units[/tex]
Hence, Perimeter of the rhombus is 20 units.
