In rhombus ABCD,AC = 15 and BD = 36. Find the | vedclass

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(C) 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

$78$

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(C) In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.Let the diagonals $AC$ and $BD$ intersect at point $O$.Then,$AO = \frac{AC}{2} = \frac{15}{2} = 7.5$ and $BO = \frac{BD}{2} = \frac{36}{2} = 18$.In the right-angled triangle $	riangle AOB$,by the Pythagorean theorem:$AB^2 = AO^2 + BO^2$$AB^2 = (7.5)^2 + (18)^2$$AB^2 = 56.25 + 324 = 380.25$$AB = \sqrt{380.25} = 19.5$.The perimeter of a rhombus is $4 	imes 	ext{side}$.Perimeter $= 4 	imes 19.5 = 78$.

In rhombus $ABCD$,$AC = 15$ and $BD = 36$. Find the perimeter of rhombus $ABCD$.

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