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two sides of a pentagon have a length of (3x-2)cm and three sides have a length of (2x+4)cm. If the perimeter is 104 cm, find the length of the longest side.

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The perimeter is the sum of all sides.
[tex]2(3x-2)+3(2x+4)=104 \\ 6x-4+6x+12=104 \\ 12x+8=104 \ \ \ |-8 \\ 12x=96 \ \ \ |\div 12 \\ x=8 \\ \\ 3x-2=3 \times 8-2=24-2=22 \\ \\ 2x+4=2 \times 8+4=16+4=20[/tex]

Two sides have a length of 22 cm, three sides have a length of 20 cm.

The longest side is 22 cm long.
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