Math CentralQuandaries & 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?

Stephen La Rocque.

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