The perimeter of a non-square rhombus is 20 , | vedclass

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(D) Let the rhombus be $ABCD$ with diagonals $AC$ and $BD$ intersecting at $O$.The perimeter of the rhombus is $20 \, cm$.Side of the rhombus $(s) = \

Vedclass · Accepted Answer

$24$

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(D) Let the rhombus be $ABCD$ with diagonals $AC$ and $BD$ intersecting at $O$.The perimeter of the rhombus is $20 \, cm$.Side of the rhombus $(s) = \frac{20}{4} = 5 \, cm$.Let diagonal $d_1 = BD = 8 \, cm$. Since diagonals of a rhombus bisect each other at right angles,$OB = \frac{d_1}{2} = 4 \, cm$.In the right-angled triangle $	riangle AOB$,by Pythagoras theorem:$OA^2 + OB^2 = AB^2$$OA^2 + 4^2 = 5^2$$OA^2 + 16 = 25$$OA^2 = 9 \implies OA = 3 \, cm$.Therefore,the other diagonal $d_2 = AC = 2 	imes OA = 2 	imes 3 = 6 \, cm$.Area of the rhombus $= \frac{1}{2} 	imes d_1 	imes d_2 = \frac{1}{2} 	imes 8 	imes 6 = 24 \, cm^2$.

The perimeter of a non-square rhombus is $20 \, cm$. One of its diagonals is $8 \, cm$. The area of the rhombus is.........$cm^2$

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