the sides of an acute triangle are x, 35, and 37, where x is the shortest side. find the range of possible values for x and express it as an inequality.
To find the range of possible values for x, we need to analyze the given information about the sides of the acute triangle.
In any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This property is known as the Triangle Inequality Theorem.
Based on this theorem, we can form the following inequalities:
x + 35 > 37 -> x > 2 (since 37 - 35 = 2)
x + 37 > 35 -> x > -2 (since 35 - 37 = -2)
35 + 37 > x -> 72 > x
Combining these inequalities, we can conclude that:
-2 < x < 2
Therefore, the range of possible values for x can be expressed as the inequality -2 < x < 2.