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The longest side of a triangle is three ...

The longest side of a triangle is three times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

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The correct Answer is:
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Let the minimum length of third side of triangle be x cm .
`:. "Largest side " = x + 2 cm `
and largest side `= 3 xx` smallest side
`x + 2 = 3 xx `smallest side
Smallest side = ` (x + 2)/(3) cm `
So , sides of triangle `= (x +2 ) /(3) , x , x + 2`
`:.` Perimeter of triangle
`= (x + 2)/(3) | x | x + 2`
`= ((x + 2) + 3x + 3x + 6 )/(3) = (7x + 8 )/(3)`
According to the problem,
`(7x + 8) /(3) ge 61`
`rArr 7x + 8 ge 183`
`rArr 7x ge 175`
`rArr x ge 25`
Therefore, minimum length of third side should be 25 cm.
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