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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

Verified Answer :

20 units im shure i took the test'

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

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

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

So, Perimeter of rhombus is given by

\(4\times Side\\\\=4\times 5\\\\=20\ units\)

Hence, Perimeter of the rhombus is 20 units.


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