jimmyjamesdonkey wrote:

Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?

I. 3

II. 9 √3

III. 13.5

(A) I only

(B) II only

(C) III only

(D) II and III

(E) I, II, and III

This problem is testing us on the triangle inequality theorem in which the sum of the lengths any two sides of a triangle MUST be greater than that of the third side. Let’s test each Roman numeral to determine which could be a possible side length of AB. Keep in mind that AC = 6 and BC = 9.

I. 3

Since 6 + 3 IS NOT greater than 9, 3 cannot be the length of side AB.

II. 9√3

9√3 is roughly equal to 9 x 1.7 = 15.3, and since 6 + 9 IS NOT greater than 15.3, 9√3 cannot be the length of side AB.

III. 13.5

Since 6 + 13.5 IS greater than 9, 13.5 + 9 IS greater than 6, and 9 + 6 IS greater than 13.5; thus, 13.5 could be the length of side AB.

Answer: C

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