Question

Find the perimeter of a rhombus having two consecutive vertices at (2, 5) and (-1, 3)

Answer 1

A rhombus is just a parallelogram, but distinct from other parallelograms, a rhombus, though its sides may be slanted, the length of each side is exactly the same.

now, what's the length of that segment from (2,5) to (-1,3)?

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ 5}})\quad % (c,d) &({{ -1}}\quad ,&{{ 3}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{(-1-2)^2+(3-5)^2}\implies d=\sqrt{(-3)^2+(-2)^2} \\\\\\ d=\sqrt{9+4}\implies d=\sqrt{13}$

now, that's just that one side, however, all 4 sides in a rhombus are the same length, therefore, its perimeter is just that added four times.