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Re: ABCD is a square with side length 12 ∠CEF is a right angle D [#permalink]
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This question involves pythagoreas theorem. After calculating all the sides, we can calculate the perimeters.
dc = 12
de = 5
ec = \sqrt{167}
ef = \sqrt{58}
fc = \sqrt{225}
af = 3
fb = 9
bc = 12
ae = 7

17+ \sqrt{167} [<] 15 + \sqrt{58} + \sqrt{167}
Qb>Qa
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Re: ABCD is a square with side length 12 ∠CEF is a right angle D [#permalink]
Mrtitsupatsundown wrote:
The question has already been solved above. Mine is more of an observation based solution that requires no calculations.
The triangles in question share EC as a side. The difference being that for DEC, it is the hypotenuse and for FEC, it is not. Now, the hypotenuse is always the biggest side in a triangle and in FEC, CF will be bigger than the other two side. Therefore, the perimeter of FEC will be greater than that of DEC


This is the best approach :blushing:
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Re: ABCD is a square with side length 12 ∠CEF is a right angle D [#permalink]
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