Rope slack

Between two streets 20 m away give the lamp, which is in the middle and hanging 60 cm bellow the taut rope. Can be done with 20.5 meters rope?

Result

Solution:

$(x/2)^2 = (20/2)^2 + 0.6^2 \ \\ (x/2)^2 = 100.36 \ \\ x/2 = 10.017983829095 \ \\ x = 20.035967658189 \ m \ \\ x < 20.5 \ m \ \\$

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