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The longest side of a triangle is three times the shortest side and the third side is 2cm shorter than the longest side if the perimeter of the triangles at least 61cm, find the minimum length of the shortest side.
  • a)
    16 cm
  • b)
    11 cm
  • c)
    61 cm
  • d)
    9 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The longest side of a triangle is three times the shortest side and th...
Let the shortest side of the triangle be x cm.
Then, the longest side will be 3x and the third side will be 3x − 2. 
∴ Perimeter of the triangle ≥ 61
⇒ x + 3x + 3x − 2 ≥ 61
⇒ 7x ≥ 61 + 2
 Dividing throughout by ⇒ x ≥ 9( Dividing throughout by 7)
Hence, the minumum length of the shortest side is 9 cm.
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Most Upvoted Answer
The longest side of a triangle is three times the shortest side and th...
Solution:

Let's assume the shortest side of the triangle is x cm.

According to the given information:
- The longest side is three times the shortest side, so it would be 3x cm.
- The third side is 2cm shorter than the longest side, so it would be (3x - 2) cm.

The perimeter of a triangle is the sum of all its side lengths. So, the perimeter of this triangle would be x + 3x + (3x - 2) cm, which simplifies to 7x - 2 cm.

Since the perimeter of the triangle is at least 61 cm, we can set up the following inequality:
7x - 2 ≥ 61

Now, let's solve this inequality to find the minimum length of the shortest side:

7x - 2 ≥ 61
7x ≥ 63
x ≥ 9

Therefore, the minimum length of the shortest side is 9 cm.

So, option D, 9 cm, is the correct answer.
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