Isosceles Triangle how to find the base?

Question

Two sides of a triangle each have length of $5$. All of the following could be the length of the third side Except.

$(A)\quad 1$

$B \quad 3$

$C \quad 4$

$(D) \quad 7.07 \text{ or } \sqrt50$

$(E) \quad 10$

Do I use the formula $2 \sqrt{L^{2}}-A^2$ in order to find the base?

Answer 1

The answer is E , beacause then "the triangle will be straight line"(in the sense both the equal sides will lie on the base with the vertex angle i.e. the angle between the equal sides being $\pi$).

Using this type of idea you can also derive the celebrated trianle inequality which says,

"Sum of any 2 sides of a triangle is always grater than the third side".

Answer 2

HINT: If you lay two $5$ inch rods end to end in a straight line, how long is that line?

(Note that since the question explicitly tells you that four of the five answers are possible lengths, it cannot be possible to determine the length of the base by some formula!)