# 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

Last updated date: 19th Mar 2023

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Answer

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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 = \dfrac{{\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} $.

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 = \dfrac{{\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} $.

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