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Suppose the shorter side is 2x cm.

Then the longer side is 3x cm

By Pythagoras, (2x)2 + (3x)2 = 262

ie 4x2 + 9x2 = 262

so that 13x2 = 262

x2 =52

so that x = 2*sqrt(13)

Then perimeter = 10x = 20*sqrt(13)

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