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(a)
Write and solve three inequalities to express the relationship among the measures of the sides of the
(a)
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Answer to Problem 36PPS
Three possible inequalities are:
Explanation of Solution
Given:
The triangle:
Concept Used:
The Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.
The three possible inequalities are:
Calculation:
Solve all the inequalities separately:
Thus, three possible inequalities are:
(b)
Find four possible lengths for the third side of the triangle.
(b)
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Answer to Problem 36PPS
The possible 4 values of the third side are: 6, 9, 10, 11
Explanation of Solution
Given:
The triangle:
Concept Used:
The Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.
Three possible inequalities are:
The possible four values of the third side are: 6, 9, 10, 11
Thus, the possible 4 values of the third side are: 6, 9, 10, 11
(c)
Write a compound inequality for the possible values of x.
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 36PPS
The compound inequality for the possible values of x is
Explanation of Solution
Given:
The triangle:
Concept Used:
The Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.
The compound inequality for the possible values of x is
Thus, the compound inequality for the possible values of x is
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