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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 \(cc_2\).

Answer :

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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