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?

Answer 1

Answer: 20 unit.

Step-by-step explanation:

Since, Here the vertices of the rhombus defg are d(1, 4), e(4, 0), f(1, –4), and g(–2, 0).

Where, de, ef, fg, gd are sides of the rhombus defg.

By the distance formula,

$de = \sqrt{(4-1)^2+(0-4)^2}$

$=\sqrt{3^2+4^2}$

$=\sqrt{9+16}$

$=\sqrt{25}$

$= 5$

Thus, the side of rhombus = 5

By the property of rhombus,

de =  ef = fg = gd = 5 unit.

Thus, the perimeter of the given rhombus defg = de +  ef + fg + gd = 5+5+5+5 = 20 unit

Answer 2

Using the distance formula to calculate the length of each side, we find that each side is 5. Since all of the sides are equivalent, the perimeter is 20.