Question

Calculate the perimeter of rhombus whose diagonals are 12 cm and 5 cm long.
A.13 cm
B.26 cm
C.39 cm
D.52 cm

Answer 1

Hint: Rhombus is a quadrilateral whose four sides have the same length and the diagonals intersect at ${90}^{\circ }$. The perimeter of the rhombus $=2\sqrt{{d_1}^2+{d_2}^2}$.

Complete step-by-step answer:
Given,
Length of diagonal $d_1$ = 12 cm
Length of diagonal $d_2$ = 5 cm
We know that,
Perimeter of rhombus $=2\sqrt{{d_1}^2+{d_2}^2}$
Where $d_1$ and $d_2$ are the lengths of the diagonals.
Substitute the values of the
$=2\sqrt{{12}^2+5^2}$
$=2\sqrt{144+25}$
$=2\sqrt{169}$
$=2\times 13$
$=26cm$
Hence option B is correct.

Note: Generally the perimeter of the rhombus of given side of length S $=4\times S$. We know that the relation length of side and lengths of the diagonals that is $S={\displaystyle \frac{\sqrt{{d_1}^2+{d_2}^2}}{2}}$$\therefore$ Perimeter of rhombus of given lengths of diagonals $=2\sqrt{{d_1}^2+{d_2}^2}$.