Question

The vertices of rhombus DEFG are D(1, 4), E(4, 0), F(1, –4), and G(–2, 0).

What is the perimeter of the rhombus?

units

Answer 1

20 units im shure i took the test'

Answer 2

Answer: Perimeter of the rhombus is 20 units.

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

`D=√((x_2-x_1)^2+(y_2-y_1)^2)\\\\D=√((4-1)^2+(0-4)^2)\\\\D=√(3^2+4^2)\\\\D=√(9+16)\\\\D=√(25)\\\\D=5\ units`

Since it is a rhombus all sides will be equal to each other,

So, Perimeter of rhombus is given by

`4* Side\\\\=4* 5\\\\=20\ units`

Hence, Perimeter of the rhombus is 20 units.