the perimeter of a triangle is 23 cm. all side lengths are integers. if one side measures 5cm, what is the length of the largest possible side?
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To find the length of the largest possible side of the triangle, we need to consider the properties of triangles and use the given information.
Let's denote the lengths of the three sides of the triangle as a, b, and c. Given that the perimeter of the triangle is 23 cm, we can write the equation:
a + b + c = 23
From the given information that one side measures 5 cm, we can assume that this side is the smallest side. Without loss of generality, let's assume a = 5 cm.
Substituting the value of a in the equation, we have:
5 + b + c = 23
Now, let's focus on finding the largest possible value for the other two sides. Since all the side lengths are integers, we want to maximize the sum of b and c.
To maximize the sum b + c, we want b and c to be as close to each other as possible. This means their difference should be minimized. So, let's assume b = c.
Substituting b = c in the equation, we get:
5 + b + b = 23
2b + 5 = 23
2b = 23 - 5
2b = 18
b = 9
Therefore, the largest possible length for the other side is 9 cm.
In summary, if one side of the triangle measures 5 cm and the perimeter of the triangle is 23 cm, the length of the largest possible side is 9 cm.