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The longest side of a triangle is twice the shortest side and the third side is 2 cm longer than the shortest side. If the perimeter of the triangle is more than 166 cm, then find the minimum length of the shortest side.

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Let the length of shortest side be x cm.
According to the given information,
Longest side = `2 xx" Shortest side"`
=2x cm
and third side = 2+ Shortest side
=(2+x) cm
Perimeter of triangle `=x+2x+(x+2)=4x+2`
According to the question,
Perimeter ` gt 166 ` cm
` rArr 4x+2 gt 166`
`rArr 4x gt 166-2`
`rArr 4x gt 164`
`:. x gt (164)/4=41 ` cm
Hence, the minimum length of shortest side be 41 cm.

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