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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
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
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