# Is there a triangle whose side lengths are 2 cm, 3 cm and 4 cm?

September 26, 2021 | education

| To solve this problem, consider the triangle inequality. The triangle inequality says that the sum of the two sides of the triangle must be greater than the third side. Let’s designate the sides of the triangle as a, b and c, then: a + b> c; a + c> b; b + c> a. Substitute the data on the condition of the value in the inequality (a = 2 cm, b = 3 cm, c = 4 cm): 2 + 3> 4 ⇒ 5> 4; 2 + 4> 3 ⇒ 6> 3; 3 + 4> 2 ⇒ 7> 2. All three inequalities are fulfilled, therefore, a triangle with sides, the lengths of which are equal to 2 cm, 3 cm and 4 cm, exists.

Answer: exists.

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