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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 triangles at least 61 cm, find the minimum length of the shortest side.

Text Solution

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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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