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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 in cm. of the shortest side.

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Solution

Let the length of the shortest side of the triangle be x cm.
Then length of the longest side =3x cm.
Thus the length of the third side =(3x2) cm.
Since the perimeter of the triangle is at least 61 cm,
x+3x+(3x2) 61
7x261
7x61+2
7x63
x9
Thus the minimum length of the shortest side is 9 cm.

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