If the sum of the lenghts of two sides of a triangle is 15, what is the largest possible integral value for the third side?
The sum of any two sides of a triangle must be greater than the third side
so if the third side is x
x < 15
Since you want x to be an integer,
x = 14
the largest possible value for the third side is 14
what is the value of x , if one lenght is 16, and the other one is 23
To find the largest possible integral value for the third side of a triangle when the sum of the lengths of two sides is given, we need to apply the triangle inequality theorem.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
In this case, the sum of the lengths of the two sides is given as 15. Let's assume the lengths of the two sides are x and y, such that x + y = 15.
To find the largest possible integral value for the third side, we need to maximize the value of the third side. This occurs when the lengths of the two sides are as close as possible to each other.
To maximize the value of the third side, we can assume that the two sides are equal, i.e., x = y. In this case, the sum of the lengths of the two sides would be 2x = 15, which gives us x = y = 7.5.
However, since the lengths of sides in a triangle must be real numbers, we cannot have a side length of 7.5.
As a result, we can take the largest possible integral value for the third side as the floor of half the sum of the lengths of the two sides, i.e., x = y = floor(15/2) = 7.
Therefore, the largest possible integral value for the third side of the triangle is 7.