A triangle has sides measuring 8 inches and 12 inches. If x represents the length in inches of the third side, which inequality gives the range of possible values for x?A.4 < x < 20B.4 ≤ x ≤ 20C.8 < x < 12D.8 ≤ x ≤ 12
Question
A triangle has sides measuring 8 inches and 12 inches. If x represents the length in inches of the third side, which inequality gives the range of possible values for x?A.4 < x < 20B.4 ≤ x ≤ 20C.8 < x < 12D.8 ≤ x ≤ 12
Solution
The answer is A. 4 < x < 20.
Here's why:
In a triangle, the length of any side must be less than the sum of the lengths of the other two sides, and greater than the difference of the lengths of the other two sides.
So, if we have a triangle with sides measuring 8 inches and 12 inches, the third side (x) must be less than 8 + 12 = 20 inches and greater than 12 - 8 = 4 inches.
Therefore, the range of possible values for x is 4 < x < 20.
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