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Question
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.
Solution
Let the length of the shortest side of the triangle be x cm.
Then, the length of the longest side = 3x cm
Length of the third side = (3x – 2) cm
Since the perimeter of the triangle is at least 61 cm,
x cm + 3x cm + (3x - 2) cm ≥ 61cm
⇒ 7x - 2 ≥ 61
⇒ 7x ≥ 61 + 2
⇒ 7x ≥ 63
⇒ `(7x)/7 ≥ 63/7`
⇒ x ≥ 9
Thus, the minimum length of the shortest side is 9 cm.
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