Perimeter of the polygon

Geometry Level 2

The triangles A B C ABC and D E F DEF are equilateral of sides 14 cm and 13 cm, respectively. What is the perimeter of the polygon P Q R S T U PQRSTU ?


The answer is 27.

Luiz Claudio by Luiz Claudio , 19, Brazil

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2 solutions

All the corner triangles are equilateral. Assuming the lengths of sides AP and PQ as x and y respectively, we get QB=a-x-y=QR, RD=RS=b-a+x, CS=ST=a-b+y, TE=TU=b-x-y, where AB=a and DE=b (side lengths of the triangles ABC and DEF). Adding up, we get the required perimeter equal to x+y+a-x-y+b-a+x+a-b+y+b-x-y=a+b=13+14=27

1 Helpful 0 Interesting 2 Brilliant 0 Confused

nice solution... sir please do use LATEX for better representation..

nibedan mukherjee - 2 years, 2 months ago

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I use smartphone, not a computer. I tried once, but the things didn't work. Sorry for the inconvenience. Stay blessed.

A Former Brilliant Member - 2 years, 2 months ago
peaceGiant Giant
Apr 29, 2019

Every triangle in the image is equilateral, hence side P U PU is the same as A U AU ; S T = T C ST=TC , so we get P U + U T + T S = A C PU+UT+TS=AC . Also S R = D R SR=DR ; P Q = F Q PQ=FQ ; S R + R Q + P Q = D F SR+RQ+PQ=DF . Conclusion: A C + D F = 14 + 13 = 27 AC+DF=14+13=27

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