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Step-by-step explanation:
We know the diagonals of a rhombus bisect each other perpendicularly. And sides of rhombus are equal.
=>angle(IOR) = angle(COE) = angle(ROE) = angle(IOC)=90°
=>IO = OE and RO = OC
From IO = OE we get 5 = x+2
=>x = 5-2 = 3
=>x = 3
From CO = OR we get 12 = y+x
=>Put value of x=3
=>12 = y+3
=>y = 12-3 = 9
=>y = 9
Now take triangle(ROE) here angle(ROE) = 90°
Using Pythagoras theorem
(RO)^2 + (EO)^2 = z^2
RO = x+y = 9+3 = 12
EO = 5
=>12^2 + 5^2 = z^2
=>144 + 25 = z^2
=>z = √(169) (as, √169 = 13)
=>z = 13
Now the perimeter is sum of all sides which are equal to each other. So, perimeter is (4×z).
=>Perimeter = 4×13
=>Perimeter = 52 units
Hope it helps...
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