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Chapter 1: Q52. (page 45)

For exercises 51 and 52, use the following information.

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.

51. Write a compound inequality to describe the range of possible measures for side cin terms of aand b. Assume that a>b>c. (Hint: Solve each inequality you wrote in exercise 51 for c)

Short Answer

Expert verified

A compound inequality to describe the range of possible measures for side c in terms of aand b isa-b<c<a+b.

Step by step solution

01

– Description of step.

Solvea+c>b. Subtract a to solve for c from each side ofa+c>bto solve for c.

a+c鈭�a>b鈭�ac>b鈭�a

02

– Description of step.

Solve b+c>a. Subtract bfrom each side of b+c>ab+c>ato solve for c.

b+c鈭�b>a鈭�bc>a鈭�b

03

– Description of step.

From a+b>c, c>b-aand c>a-bit can be concluded that a-b<c<a+b.

Therefore, a compound inequality to describe the range of possible measures for sidecin terms of aand bis a-b<c<a+b.

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