Home > Geometry > Solving Problems with Similar and Congruent Triangles

Can the sides of a triangle have lengths 1, 2, and 8?

Answer 1

Claire Akin

The simple answer is no.

In a triangle , the sum of any two sides is greater than the third side.

Let's try the three possible ways

#1) 1+8>2#

#=> 9>2#

It's correct.

#2) 2+8>1#

#=> 10>1#

It's also correct.

#3)1 + 2 > 8#

#=>3>8#

But it is not correct.

This is not possible because the length of third side is greater than the sum of length of other two sides.

Thus , such a triangle is not possible.

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Answer 2

James Atkins

No, the sides of a triangle cannot have lengths 1, 2, and 8 because the sum of the lengths of any two sides of a triangle must be greater than the length of the third side according to the triangle inequality theorem. In this case, 1 + 2 is not greater than 8, violating the theorem. Therefore, a triangle with sides of lengths 1, 2, and 8 cannot exist.

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Answer from HIX Tutor

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