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Question
The longest side of a triangle is three times the shortest side and 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.
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Solution
Let the shortest side of the triangle be x cm.
Then, the longest side will be 3x and the third side will be 3x − 2.
\[\therefore \text{ Perimeter of the triangle } \geq 61\]
\[ \Rightarrow x + 3x + 3x - 2 \geq 61\]
\[ \Rightarrow 7x \geq 61 + 2\]
\[ \Rightarrow x \geq 9 (\text{ Dividing throughout by } 7)\]
\[\text{ Hence, the minumum length of the shortest side is 9 cm } .\]
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