What is the largest possible value of the fourth side length of a quadrilateral with side lengths of 12 cm, 16 cm, 25 cm, and x cm, where x is unknown?
To find the largest possible value of the fourth side length, we can use the Triangle Inequality Theorem. According to this theorem, in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
So, in this case, to determine the largest possible value of the fourth side length, we need to check whether the sum of the lengths of the three known sides is greater than the fourth side length. If it is, then we can consider that length as the largest possible value. If it isn't, then there is no valid quadrilateral with those side lengths.
Let's calculate the sum of the lengths of the three known sides:
12 cm + 16 cm + 25 cm = 53 cm
Now we need to check if the sum of these three sides is greater than the fourth side length (x cm):
53 cm > x cm
Therefore, the largest possible value of the fourth side length (x cm) is 53 cm.
To find the largest possible value of the fourth side length, we need to consider the Triangle Inequality Theorem for quadrilaterals:
In any quadrilateral, the sum of the lengths of any three sides must be greater than the length of the fourth side.
Let's apply this theorem to our problem:
12 + 16 + 25 > x
41 + 25 > x
66 > x
Therefore, the largest possible value for x is 66 cm.