In rhombus PQRS,PR = 9 and QS = 12. Find the | vedclass

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(C) In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.Let the diagonals $PR$ and $QS$ intersect at point $O$.Since the diago

Vedclass · Accepted Answer

$30$

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(C) In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.Let the diagonals $PR$ and $QS$ intersect at point $O$.Since the diagonals bisect each other,$PO = OR = \frac{PR}{2} = \frac{9}{2} = 4.5$ and $QO = OS = \frac{QS}{2} = \frac{12}{2} = 6$.In the right-angled triangle $	riangle POQ$,by the Pythagorean theorem:$PQ^2 = PO^2 + QO^2$$PQ^2 = (4.5)^2 + (6)^2$$PQ^2 = 20.25 + 36 = 56.25$$PQ = \sqrt{56.25} = 7.5$.Since all sides of a rhombus are equal,the perimeter is $4 	imes PQ$.Perimeter $= 4 	imes 7.5 = 30$.

In rhombus $PQRS$,$PR = 9$ and $QS = 12$. Find the perimeter of rhombus $PQRS$.

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