SOLUTION: Can the side lengths of a triangle be 2, 4 and 8? Justify your answer.

Question 1200278: Can the side lengths of a triangle be 2, 4 and 8? Justify your answer.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

A triangle with such side lengths does not exist,

because the triangle inequality is not held: the sum of the side lengths 2 and 4
is less than the side length of the third side 8.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Imagine having three straight sticks with lengths 2, 4, and 8 inches. Try making a triangle with those sticks.

Lay the 8-inch stick down, then tie one end of the 4-inch stick to one end of the long stick and one end of the 2-inch stick to the other end of the long stick. Then rotate the two short sticks to try to make them meet. They can't, because the sum of their lengths is less than the length of the long stick.

In order to form a triangle, the sum of the lengths of the two shortest sticks must be greater than the length of the longest stick.

That is exactly what the triangle inequality says: the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the longest side.

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