see diagram in attachment
a rhombus is a 4 sided figure with 4 equal length sides
so if we can find the length of 1 side and multiply it by 4, we get the perimiter
you can draw 2 lines to make 4 similar triangles
we can see that you can use pythagorean rule to get the length of the hypotonuse of one triangle so
so perimiter is 4*5=20 units
or you can use distance formula which is basically the pythatorean theorm
from W to X, that is from (-3,1) to (1,4)
![d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%7D)
![d=\sqrt{(-3-1)^2+(1-4)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-3-1%29%5E2%2B%281-4%29%5E2%7D)
![d=\sqrt{(-4)^2+(3)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-4%29%5E2%2B%283%29%5E2%7D)
![d=\sqrt{16+9}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B16%2B9%7D)
![d=\sqrt{25}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B25%7D)
![d=5](https://tex.z-dn.net/?f=d%3D5)
4*5=20, so perimiter is 20 units