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.

Answer 1

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.