Answer :
Final answer:
The possible lengths for the third side of a triangle with two sides measuring 23 and 17 must satisfy the Triangle Inequality Theorem and be less than their sum (40). The valid options given are 17, 20, and 27.
Explanation:
The question involves determining the possible lengths of the third side of a triangle given the lengths of the other two sides. To find the possible measures of the third side, we apply 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.
Given sides of lengths 23 and 17, we can set up inequalities with an unknown third side length, let's call it x. The inequalities will look like this:
- 23 + 17 > x
- 23 + x > 17
- 17 + x > 23
From the first inequality, we learn that x must be less than 40. The second and third inequalities are always true for positive values of x because 23 and 17 are already greater than 17 and 23, respectively. Combining these, the possible range for x is:
0 < x < 40
Therefore, the only values that could be the third side of the triangle from the given options are: B. 17, C. 20, and D. 27.
Learn more about Triangle Inequality Theorem here:
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