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Anuta_ua [19.1K]
4 years ago
7

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

Mathematics
1 answer:
likoan [24]4 years ago
5 0
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.
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