Sagot :
Answer:
91 cm
Step-by-step explanation:
Let x be the third side of the triangle.
As per Triangle Inequality Theorem, the sum of any two sides of the triangle is always greater than the third side of the triangle.
Hence, x must be at its minimum value.
Now, let's consider the cases below:
- Case 1: If 42 + 45 > x, then 87 > x, then the minimum value of x is negative, which is impossible to be the length of the third side of a triangle.
- Case 2: If 45 + x > 42, then the minimum value of x is -2, which is impossible to be the length of the third side of a triangle and doesn't satisfy the triangle inequality theorem.
- Case 3: If 42 + x > 45, then the minimum value of x is 4, which satisfies the triangle inequality theorem.
Therefore, the minimum value of the perimeter of the triangle is 42 + 45 + 4 = 91.
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