The diagonals of a rhombus are 16,cm and 30,c | vedclass

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Question

(A) Let the diagonals of the rhombus be $d_1 = 16\,cm$ and $d_2 = 30\,cm$.In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.

Vedclass · Accepted Answer

$68$

Vedclass · Answer

(A) Let the diagonals of the rhombus be $d_1 = 16\,cm$ and $d_2 = 30\,cm$.In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.Let the side of the rhombus be $a$. The diagonals divide the rhombus into four congruent right-angled triangles.The legs of these triangles are half the lengths of the diagonals: $d_1/2 = 8\,cm$ and $d_2/2 = 15\,cm$.Using the Pythagorean theorem: $a^2 = (8)^2 + (15)^2$.$a^2 = 64 + 225 = 289$.$a = \sqrt{289} = 17\,cm$.The perimeter of a rhombus is $4 	imes 	ext{side} = 4 	imes 17 = 68\,cm$.

The diagonals of a rhombus are $16\,cm$ and $30\,cm$. Find its perimeter. (in $,cm$)

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