Prove that one side of the triangle is less than half of its perimeter.
| December 13, 2020 | education
Let the sides of the triangle be a, b, c. Let us prove that (a + b + c) / 2> a. Let’s multiply both sides of the inequality by 2: a + b + c> 2a <=> b + c> a. By the property of a triangle, the sum of its two sides is greater than its third side. Hence, it is true that b + c> a. Then it is true that one side of the triangle is less than its half-perimeter.
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