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Answer :
Final answer:
To find the length of the third side of a triangle where one side is 38.5 inches and the second is 30 inches, we can use the Pythagorean theorem if the triangle is right-angled. The third side, or the hypotenuse, can be calculated by squaring both sides, adding the results, and taking the square root of the sum, resulting in approximately 48.81 inches.
Explanation:
To calculate the length of the third side of a triangle, we must know if the triangle is right-angled because if it is, we can use the Pythagorean theorem. If one side is 38.5 inches and the second side is 30 inches, and the triangle is right-angled, the length of the third side, which we'll call c, could be computed assuming these are the two legs of the triangle.
Using the Pythagorean theorem, which states a² + b² = c², where a and b are the legs of the right triangle and c is the hypotenuse, we can find the length of the hypotenuse.
Here's the calculation if the given sides are the two legs of a right-angled triangle:
- Square both given lengths: 38.5² + 30²
- Add the squares: 1482.25 + 900 = 2382.25
- Find the square root of the sum: √2382.25
- Calculate the square root to get the length of the third side: 48.81 inches (rounded to two decimal places)
If the triangle is not right-angled, then we cannot determine the length of the third side without additional information.
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Answer:
The length of the third side must be less than 68.5 inches
Step-by-step explanation:
Given:
- One side of the triangle is 38.5 inches, and the second side is 30 inches.
Calculate the length of the third side.
We can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
38.5 + 30 > x
68.5 > x
So, the length of the third side must be less than 68.5 inches.
