Question

calculating the perimeter of a rhombus
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

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate side - length using points D(1,4) and E(4,0)

Substitute $x_1 = 1,y_1 = 4,x_2 = 4,y_2 = 0$ into the distance formula:
\[

$$\begin{align*} d&=\sqrt{(4 - 1)^2+(0 - 4)^2}\\ &=\sqrt{3^2+( - 4)^2}\\ &=\sqrt{9 + 16}\\ &=\sqrt{25}\\ &=5 \end{align*}$$

\]

Step3: Calculate perimeter of rhombus

Since all sides of a rhombus are equal, and perimeter $P = 4s$ (where $s$ is the side - length). Here $s = 5$, so $P=4\times5 = 20$.

Answer:

20