Sides of a Triangle Practice

Question

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5 of 55 of 5 Items

Question
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A horizontal number line is labeled from left to right with the numbers 30 to 100 in increments of 10. Open circles are shown on the number line at labeled values of 36 and 92. The number line is shaded between the open circles.

x is the length in inches of the third side of a triangle. The range of all possible values of x is shown on the number line. Which of the following options has possible lengths of the other two sides of the triangle?

(1 point)
Responses

42 inches and 50 inches

28 inches and 64 inches

36 inches and 92 inches

48 inches and 76 inches

Answer 1

The answer is 36 inches and 92 inches.

Answer 2

false

Answer 3

My apologies for the incorrect answer. Since the range of possible values for x is shown on the number line between 36 and 92, the possible lengths for the other two sides of the triangle must fall within this range. However, without further information or measurements, we cannot determine the exact lengths of the other two sides. Therefore, the correct answer is that there is not enough information given to determine the possible lengths of the other two sides of the triangle.

Answer 4

If a and b are the lengths in inches of the other two sides of a triangle, then it must be true that |a−b| < x < a+b
.

Answer 5

Yes, that is correct. According to the Triangle Inequality Theorem, for any triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side. Mathematically, this can be written as:

|a - b| < c < a + b

In this case, x represents the length of the third side, so the correct inequality would be:

|a - b| < x < a + b

This means that the length of x must be greater than the difference between the other two side lengths (|a - b|) and less than the sum of the other two side lengths (a + b).