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 in cm be x.

Then, the length of the longest side in cm = 3x

Length of the third side in cm = (3x - 2)

Since the perimeter of the triangle is at least 61 cm,

Therefore,

x + 3x + (3x - 2) ≥ 61

⇒ 7x - 2 ≥ 61

⇒ 7x ≥ 61 + 2

⇒ 7x ≥ 63

⇒ x ≥ 63/7

⇒ x ≥ 9

Thus, the minimum length of the shortest side is 9 cm

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 25

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

Summary:

A linear inequation x + 3x + (3x - 2) ≥ 61 can be formed. We have found that the minimum length of the shortest side is 9 cm