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The longest side of a triangle is 3 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.
  • a)
    9 cm
  • b)
    11 cm
  • c)
    13 cm
  • d)
    14 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The longest side of a triangle is 3 times the shortest side, and the t...
Let x cm be the length of the shortest side of the triangle.
∴ According to the question, length of the longest side = 3x cm
Length of the third side = (3x – 2) cm
The least perimeter of the triangle = 61 cm (given)
Thus, x + 3x + (3x – 2) cm ≥ 61 cm
= 7x – 2 ≥ 61
= 7x ≥ 63
Dividing by 7 on both sides, we get;
= 7x/7 ≥ 63/7
= x ≥ 9
Hence, the minimum length of the shortest side will be 9 cm.
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