In rhombus ABCD,AC = 18 and BD = 24. Find the | vedclass

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(B) In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.Let the diagonals $AC$ and $BD$ intersect at point $O$.Then,$AO = \fra

Vedclass · Accepted Answer

$60$

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(B) In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.Let the diagonals $AC$ and $BD$ intersect at point $O$.Then,$AO = \frac{AC}{2} = \frac{18}{2} = 9$ and $BO = \frac{BD}{2} = \frac{24}{2} = 12$.In the right-angled triangle $	riangle AOB$,by the Pythagorean theorem:$AB^2 = AO^2 + BO^2$$AB^2 = 9^2 + 12^2$$AB^2 = 81 + 144 = 225$$AB = \sqrt{225} = 15$.The perimeter of a rhombus is given by $4 	imes 	ext{side}$.Perimeter $= 4 	imes 15 = 60$.

In rhombus $ABCD$,$AC = 18$ and $BD = 24$. Find the perimeter of rhombus $ABCD$.

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