Answer :
Final answer:
To find the length of side X in the given geometric shape, we use the Triangle Inequality Theorem to check if it forms a valid triangle. Then, we use the triangle's perimeter formula to find the length of side X, which is 0 feet in this case.
Explanation:
To find the length of side X in the given geometric shape, we need to determine if it is a triangle or some other shape. Assuming it is a triangle, we can use the Triangle Inequality Theorem to determine if the lengths of the other sides form a valid triangle.
- Add the two smallest side lengths together: 36.6 + 33.1 = 69.7 feet
- If this sum is greater than the length of the longest side, then it is a valid triangle. Otherwise, it is not.
In this case, 69.7 feet is greater than 40.2 feet, so it is a valid triangle. Now we can use the triangle's perimeter formula to find the length of side X.
Perimeter = sum of all side lengths
Perimeter = 36.6 + 33.1 + 38.4 + 40.2
Perimeter = 148.3 feet
Since the sum of all the other side lengths is 148.3 feet, we can subtract this sum from the total perimeter to find the length of side X.
Length of side X = Perimeter - sum of other side lengths
Length of side X = 148.3 - (36.6 + 33.1 + 38.4 + 40.2)
Length of side X is therefore 148.3 - 148.3 feet = 0 feet
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