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pa help po please huhuhuhuhuhu
The length of two sides of a triangle are 42 cm and 45 cm respectively. It is known that the length of the other side is also an integer. What is the minimum perimeter of the triangle?


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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