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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.

Text Solution

Verified by Experts

The correct Answer is:
9 cm
Let the length of the shotest side of the triangle be x cm .
Then length of the longest side = 3 x cm
Length of the third side =( 3 x - 2 )cm
Since the perimter of the triangle is at least 61 cm .
`x+3x+(3x-2) ge 61`
`rArr 7x - 2 ge 61`
`rArr 7x ge 61 +2`
`rArr 7x ge 63 `
`rArr x ge 9 `
Thus the minimum lenght of the shortest side is 9 cm .
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