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Answer :
Final answer:
1. 10.0 inches & 3. 11.7 inches
The possible side lengths of the third side of the right triangle are approximately 12.7 inches and 13.1 inches.
Explanation:
To find the possible side lengths of the third side of the right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Let's call the missing side x. Using the theorem, we have 6.2^2 + 11.5^2 = x^2. Solving for x, x^2 = 6.2^2 + 11.5^2. Taking the square root of both sides, x = √(6.2^2 + 11.5^2). Evaluating the expression gives us two possible side lengths of approximately 12.7 inches and 13.1 inches, so the correct options are 1. 10.0 inches and 3. 11.7 inches.
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