B. 22>x> 6
C. 8< x < 14
D. 6 < x < 22
Answer:
D. 6 < x < 22
Step-by-step explanation:
For a triangle, the third side must be less than the sum of the other two sides and it must greater than the difference between the other two sides.
The possible length of the third side of the triangular pen, given the Triangle Inequality Theorem and two given side measures, is best described by the inequality D. 6 < x < 22.
To find the possible length of the third side of a triangle, we use the Triangle Inequality Theorem. The theorem states that the length of any side of a triangle is less than the sum of the lengths of the other two sides and greater than the absolute difference of the lengths of the other two sides. Here, we have the lengths of two sides as 14 ft and 8 ft.
So the sum of these two sides is 14 + 8 = 22 ft. The difference is |14 - 8| = 6 ft. Therefore, the length of the third side 'x' can range between the sum and the difference of the other two sides. Hence, the correct answer is D. 6 < x < 22.
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