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

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Answer 1 · 2018-03-05T03:06:37

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

$1) 1 + 8 > 2$ $1) 1+8>2$

$\Rightarrow 9 > 2$ $=> 9>2$

It's correct.

$2) 2 + 8 > 1$ $2) 2+8>1$

$\Rightarrow 10 > 1$ $=> 10>1$

It's also correct.

$3) 1 + 2 > 8$ $3)1 + 2 > 8$

$\Rightarrow 3 > 8$ $=>3>8$

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.