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The longest side of a triangle is 4 times the shortest side and the third side is 4 cm shorter than the longest side. If the perimeter of the triangle is at least 59 cm, then the minimum length of the shortest side is
  • a)
    9 cm
  • b)
    8 cm
  • c)
    7 cm
  • d)
    6 cm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The longest side of a triangle is 4 times the shortest side and the th...
Problem Analysis:
Let the shortest side of the triangle be x cm.
According to the given information, the longest side is 4 times the shortest side, so it will be 4x cm.
The third side is 4 cm shorter than the longest side, so it will be (4x - 4) cm.
The perimeter of a triangle is the sum of the lengths of all three sides.
So, the perimeter of this triangle will be x + 4x + (4x - 4) = 9x - 4 cm.

Solution:
To find the minimum length of the shortest side, we need to find the minimum value of x for which the perimeter is at least 59 cm.

Let's set up the inequality:
9x - 4 ≥ 59
9x ≥ 63
x ≥ 7

Therefore, the minimum length of the shortest side is 7 cm.

Hence, the correct answer is option 'C'.
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