The longest side of a triangle is 3 times the shortest side and the 3^rd side is 2cm shorter than the longest side. If the perimeter of the triangle is atleast 61cm. Find the minimum length of the shortest side.

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Let the length of the shortest side be x

Then,the length of the longest side =3x
and thrid side of the triangle = 3x-2 respectively.

According to question,

perimeter of triangle ≥61⇒x+3x−2+3x≥61⇒7x≥61+2⇒7x≥63⇒x≥637⇒x≥9∴The minimum length of the shortest side is 9 cm.

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