The three sides of a triangle

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Quandaries & Queries

The sum of the lengths of any 2 sides of a triangle must be greater than the third side. If the triangle has one side that is 11 CM, and the second side of the triangle is 4 cm less than twice the third side, what lengths do the 2nd and 3rd side have to be?
between 0000-00-00 and 9999-99-99

Let T = the length of the third side. Then the second side is T - 4.

So any two sides are greater than the remaining side. This provides 3 inequalities:

T + (T - 4) > 11
T + 11 > T - 4
(T - 4) + 11 > T

When you simplify, what do you learn about the valid range for T, the third side? Is it possible for T to be "as large as you want" or "as small as you want"?

What does that mean the valid range of the second side must be?

Cheers,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.