Problem 27 of 34geo-027
Two sides of a triangle are 6 inches and 11 inches long. Which of the following could be the length, in inches, of the third side?
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Solution walkthrough1:44
- Join the and sides at a hinge. The third side, , closes the gap between their free ends.
- Close the hinge and shrinks toward . At exactly the triangle is flat, so .
- Open the hinge and grows toward . At exactly it is flat again, so .
- So . Of the choices, only is between and .
- Traps: and are the flat cases, not triangles. is longer than , so the sides cannot reach.