study wrote:

If the lengths of the sides of a triangle are a , b , and 7, which of the following could be the value of a – b ?

I. 4

II. 7

III. 12

I only

II only

I and II only

II and III only

I, II, and III

Use the third side rule: The third side is greater than than the difference of the rest two sides and smaller than the sum of those two sides.

Suppose three sides are 3, 4, and x: (4-3) < x < (3+4).

If so, (a-b) < 7. That is (a-b) can be 4 but not 7 or 12.

A.

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