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A pentagon $abcde$ is translated north by 40 units to pentagon $a_1 b_1 c_1 d_1 e_1.$ pentagon $a_1 b_1 c_1 d_1 e_1$ is then translated east by 50 units to pentagon $a_2 b_2 c_2 d_2 e_2.$ we know the perimeter of pentagon $abcde$ is 30 units. find $cc_2.$

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LammettHash

The perimeter of the pentagon is irrelevant. The distance [tex]cc_2[/tex] is equal to the length of the hypotenuse of a triangle with legs of length 40 and 50 units. By the Pythagorean theorem,

[tex]{cc_2}^2 = 40^2 + 50^2 \implies cc_2 = \boxed{10\sqrt{41}}[/tex]

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